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3 9080 03130 2364 

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55 Massachusetts Institute of Technology 

Department of Economics 
Working Paper Series 


Henry S. Farber 

Working Paper #355 
November, 1984 

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Cambridge, MA 021 42 

Digitized by the Internet Archive 

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Forthcoming in: 

Handbook of Labor Economics 

The first version of this paper was written while the author was a Fellow at the Center for 
Advanced Study in the Behavioral Sciences. The author received support for this research 
from the National Science Foundation under Grant Nos. BNS-76-22943, SES-8207703, and 
SES-8408623 and from the Sloan Foundation as an Alfred P. Sloan Research Fellow. 
Comments by David Card, Roger Noll, Andrew Oswald and John Pencavel on related 
research are gratefully acknowledged. 

Forthcoming in: 

Handbook of Labor Economics 


Henry S . Farber 
Number 355 November 1984 

The first version of this paper was written while the author was a 
Fellow at the Center for Advanced Study in the Behavioral Sciences. 
The author received support for this research from the National 
Science Foundation under Grants Nos. BNS-76-229A3, SES-8207703, and 
SES-8408623 and from the Sloan Foundation as an Alfred P. Sloan 
Research Fellow. Comments by David Card, Roger Noll, Andrew Oswald, 
and John Pencavel on related research are gratefully acknowledged 



Henry S. Farber 

MassachuBettB Institute of Technology 

November 1984 

There 15 now a substantial body of economic research that models the 
behavior of labor unions as ma;c 1 mi zat 1 on of a well defined objective function. 
This paper presents both a selective critical survey of this literature and a 
preliminary consideration of some important problems that have not been 
addressed in the literature to date. Particular emphasis is on work that is 
operational in the sense that it has an empirical component or is amenable to 
empirical implementation. Topics surveyed include 1) the general economic 
modus operandi of labor unions in the U.S. economy; 2) the structure of 
bargaining and the efficiency of labor contracts; 3) the bargaining process 
as it relates to the identification of union objectives; and 4) empirical 
studies of union objectives. 

While much is learned from the existing literature, it is argued that a 
more general pol i t 1 cal /economi c model of union behavior is needed. This model 
would derive the objective function of the union in a consistent fashion from 
the preferences of the workers and union leaders through a well defined 
political process. Three important issues that are central to the development 
of such a model are addressed: 1) The determination of the size of the union 
and the rules used for the allocation of scarce union jobs; 2) the aggregation 
of preferences when workers are heterogeneous; and 3) the union leadership as 
an entity capable of pursuing its own goals. 

I . Introduction and Overview 

There is a large literature documenting the observed di -f -f erences between 
the union and nonunion sectors in the U.S. economy. It is well known that 
union workers earn between five and twenty--five percent more than nonunion 
workers with the same observable characteristics, with the precise -figure 
depending both on the occupation, industry, and other characteristics of the 
worker and on the level of aggregate economic activity. There are also 
important differences between union and nonunion jobs in many other 
dimensions. Some of these are: 1) non-wage benefits make up a significantly 
larger share of total compensation in the union sector than in the nonunion 
sector (Freeman, 1981); 2) the structure of compensation in the union sector 
is such that the variance of earnings is lower than in the nonunion sector 
both overall and for workers in particular occupations and industries 
(Freeman, 19B0b; Bloch and Kuskin, 197B); 3) Quits from union jobs occur at 
lower rates than quits from nonunion jobs (Freeman, 19B0a); 4) the layoff rate 
and cyclical swings in employment are larger in the union sector than -in the 
nonunion sector (Medoff, 1979); 5) Formal mechanisms for settling disputes 
between employers and their employees, often with arbitration as the ultimate 
recourse, Are more common in unionized establishments;'^ 6) The role of 
seniority in determining the order of layoffs and preference for promotion is 
greater in the union sector (Abraham and Medoff, 19B4a, 1984b); and 7) The 
working setting is more rigidly structured in the union sector (Duncan and 
Stafford, 1980). 

1. Lewis (1963) presents the first detailed empirical examination of the 
union-nonunion wage differential. Freeman and Medoff (19Bla) and Lewis (1984) 
and elsewhere in this volume present recent surveys of the vast literature on 
this topic. 

2. Card (1983) presents an interesting theoretical analysis of the role 
that grievance arbitration might play in the collective bargaining 

Overall, there has been a tremendous amount o-f e-ffort devoted to 
meaBurinq the observed di-fferences between union and nonunion jobs, and it is 
fair to say that this eHort has been success-ful. However, there has been 
less success in understanding the reasons -for these di -f -f erences , and there is 
quite a bit of controversy about what these differences mean. Are they 
accurate measures of the effects of unions, are they biased estimates of the 
effects, or are they statistical artifacts? How can these estimates be used 
to predict union response to changing economic conditions? Without a complete 
understanding of union behavior and how the outcomes of collective bargaining 
are determined it is difficult to answer these questions. 

There is a substantial body of economic research, largely theoretical 
but with a recent empirical component, on the analysis of union behavior. It 
is the purpose of this chapter to survey this literature selectively and to 
place it in perspective so that analysts may begin to answer questions raised 
by the descriptive research on labor unions and to understand the role that 
unions play in the economy. The emphasis throughout is on work that is 
operational in the sense that it has an empirical component or is amenable to 
empirical implementation. No attempt is made to be exhaustive in reviewing 
the literature. The primary focus is on fitting the existing work into a 
coherent conceptual framework and on suggesting some directions for further 
research. In order to keep the analysis and discussion tractable, the 
presentation will be restricted for the most part to a discussion of the 


3. The most attention has been paid to interpreting estimates of the 
union-nonunion wage differential. Does it actually measure the "effect" of 
unions on wages? Does unionization affect the wages of nonunion workers? Do 
unions organize the "better" workers? The extensive literature on this topic 
includes work by Lewis (1963), Rosen (1969), Schmidt and Strauss (1976), Lee 
(1978), Freeman and Medoff (1981a, 1981b), and Freeman (1984). See also the 
surveys by Lewis (1984) and elsewhere in this volume. 

determination of wages and employment as these have been the focus o-f the vast 

majority of earlier research. 

In the next section, the stage is set with a working definition of a 
labor union and a brief description of the economic modus operandi of labor 
unions in the American economy. A number of examples of unions in various 
industries within the United States are presented in order to highlight the 
role that market and legal /pol i ti cal constraints play in determining the 
environment within which unions operate. It is argued that there are three 
actors or sets of actors that must be considered in any model of the operation 
of the union sector: 1) the firm; 2) the members of the union; and 3) the 
leaders of the union. As is appropriate for an economic model, it is be 
assumed that individuals (leaders as well as members) have well defined 
objective functions that they are maximizing. In addition, it is assumed that 
the firms are profit maximizers. > 

While the union members and their leaders may be maximizers, it does not 
necessarily follow that the union, as an organization, has a well defined 
objective function. The famous debate between Ross (194B), who took the 
position that unions cannot be analyzed fruitfully as maximizing a well 
defined objective function, and Dunlop (1944), who argued the opposite, is 
recounted briefly. Basically, it is concluded that Dunlop was right in that 
it is fruitful to analyze labor unions as maximizing a well defined objective 
function but that the internal structure of the union and its political 
process, emphasized by Ross, are important determinants of the objective 

In order to continue with the analysis of union behavior the structure 

4. Of course this is at least partly because wages and employment are more 
easily quantifiable and measurable than such things as the particular terms of 
a grievance settlement procedure or a seniority preference provision. 

of barqaininq needs to be considered care-fully. In this context the structure 
o-f bargaining re+ers to the set o-f issues that are determined directly through 
the bargaining process. Two polar examples o-f bargaining structure that have 
played a prominent role in the literature on wage and employment determination 
are discussed in section III. The -first is where the parties bargain only 
over the wage leaving the firm to determine employment according to the labor 
demand schedule. The second is where the parties bargain over both the wage 
and the employment level. The optimal wage/employment outcomes of the union 
and the firm are derived in each of these cases. The more realistic 
intermediate, case where work rules and the like provide partial control over 
employment, is also addressed briefly. 

Section III also contains a discussion of the efficiency of labor 
contracts as it is related to the bargaining structure. It has been argued 

that efficiency is strongly affected by the degree to which the parties 

bargain (either explicitly or implicitly) over employment as well as wages. 

It is concluded that if only the wage is negotiated and the employer is free 

to set employment then a bargain will never be efficient. On the other hand, 

if both the wage and employment are bargained then the contract could be 

efficient. It is further argued that problems of asymmetric information and 

incentive compatibility make it likely that most unions can bargain over the 

the wage but that they can control employment imprecisely at best. Thus, it 

is concluded that labor contracts are not likely to be efficient in most 

5. Bargaining structure often has a different meaning in the industrial 
relations literature than that used here. In that context bargaining 
structure refers to the scope of the bargaining unit (the group of workers 
that bargain together). The scope of a bargaining unit can be defined by such 
things as industry, occupation, and location. The determinants and 
implications of bargaining structure defined this way is an interesting and 
important problem, but its analysis is beyond the scope of this chapter. 

6. See, for example, Hall and Lilien (1979), McDonald and Solow (19B1), 
Ashenfelter and Brown (19B3), and MaCurdy and Pencavel (1984). 


Given an objective function -for the union, the pro-fit function o-f the 
•firm, the structure of the bargain, and the constraints posed by the economic 
environment, it is necessary to specify the process by which the parties 
bargain and reach agreement. This is the focus of section IV. The general 
framework for collective bargaining between the union and the firm is that 
they attempt to reach agreement, but if they do not agree then there is a 
strike where the union withholds its labor. The workers suffer the loss of 
wages and the firm suffers loss of output and profits. These costs of 
disagreement provide the incentive for the parties to reach agreement. A 
complete analysis of the bargaining process is beyond the scope of this study, 
but some simple models that have proven useful in empirical work are presented 

In section V a number of empirical studies that implement models of the 
outcomes of collective bargaining and that are consistent with the general 
framework are presented and discussed. These studies, though restricted to a 
small number of industries, present fairly clear evidence regarding systematic 
variation in the wage/employment bargains struck by unions and employers. The 
interpretation that is given to these results is that labor unions weight 
employment relatively heavily compared to wages in reaching an agreement. An 
alternative interpretation is that employers resist union wage demands 
successfully, resulting in what appears to be a relatively high weight on 
employment when, in fact, the union would have preferred higher wages and less 
employment. With regard to the efficiency of labor contracts, some seemingly 

7. Of course, this issue can only be settled empirically. A discussion 
of some attempts to do just that (Ashenfelter and Brown, 1983; MaCurdy and 
Pencavel , 1984) are contained in section V. 

B. See the chapter by Kennan elsewhere in this volume for a more detailed 
discussion of strikes. 

con-flicting empirical results are reconciled and conclusions are drawn 
regarding the extent to which unions in one setting can control employment in 
addition to wages. 

While much is learned -froni these studies, the sort of ad hoc objective 
function -for a labor union proposed by Dunlop and characteristic o-f most of 
the studies reviewed in section V misses a central feature of labor unions: 
their basically political nature. In order to understand the behavior of 
labor unions fully it is necessary to follow Ross's lead in considering the 
political process that a union uses to make decisions. Given an understanding 
of the internal operation of the union, it is possible to derive an objective 
■function for a union from the preferences of the members and leaders that can 
be used for the empirical investigation of union behavior. Because such a 
model is derived from the behavior of individual economic agents in a 
consistent fashion, it will be more likely to yield reliable predictions 
regarding the effects of changes in important economic variables on union 

The development and empirical implementation of a general 
pol i tical /economi c model of union behavior is no simple task, particularly 
since unions differ in the institutional framework governing the political 
process. All that are fixed across different settings are the preferences of 
the workers and some general principles relating worker preferences and the 
political process to the objective function of the union. The agenda for 
future research on union behavior must include theoretical and empirical 
analyses of these principles. The final sections of this chapter contain 
preliminary discussions of three problems that ars central to this effort. 
These discussions are meant to illustrate our current understanding of these 
problems and to suggest directions for further research rather than to present 
complete solutions. 

Section VI -focuses on an issue that is central to the analysis of union 
behavior and that has been neglected by virtually all researchers: the 
determination o-f the size oi the union. The size oi the union determines who 
the voting membership are and what their preferences over various wage- 
employment combinations are. It is argued that the size and composition of 
the union depend crucially on the rule used for the allocation of scarce union 
jobs among the membership (random, worksharing, seniority, productivity, etc.) 
and whether the union can restrict membership. , 

In section VII the problem of heterogeneity in preferences among workers 
is discussed in the context of a very simple model of union behavior, where a 
single issue is being decided (wages) and the democratic process operates 
perfectly. The central issue is how the diverse preferences of the workers 
are reconciled into a coherent objective function for the union. The median 
voter model of preference aggregation, its limitations, and its implications 
for union behavior are discussed with heterogeneity in a number of dimensions, 
including seniority and productivity. The dynamic implications of the median 
voter formulation for the size of the union are also addressed. 

In section VIII the union leadership is introduced as an entity capable 
of pursuing its own goals. This is achieved through relaxation of the 
assumption of perfect democracy. First, the polar opposite of the perfect 
democracy model is considered by assuming that the leadership of the union is 

a dictatorship constrained only by the possibility that workers will leave the 

union and by the behavior of the employer. Second, a more realistic 

intermediate case is discussed where there are costs that must be borne by an 

insurgency and where the ultimate success of an insurgency is uncertain. A 

9. The classic reference for this model of union behavior is Lewis (1959) 
Dunlop (1944) discusses the "membership function" as a constraint on union 
behavi or . 


model of leadership behavior is discussed where the leadership is attempting 
to maximize a well defined objective -function (e.g., employment, dues 
revenues) subject to the constraints of attracting members (a membership 
function as in Dunlop, 1944), a labor demand function, and the probability of 
a successful insurgency. This probability is modeled as a function of the 
preferences of the members, the policies adopted by the leadership, and the 
costs (monetary and otherwise) of an insurgency. It is concluded that the 
leadership will generally adopt a postion close to that preferred by the 
median voter unless the costs of an insurgency are very high. Thus, the oft- 
cited median voter model of union behavior may be of descriptive significance 
in a broader, range of settings than is suggested by its rather stringent set 
of underlying assumptions. 

II. Setting the Stage 

For the purposes of the discussion here, a labor union can be considered 
to be a group of workers who bargain collectively with employers regarding the 
terms and conditions of employment. These workers will generally not 
bargain themselves but will have as agents union leaders who are elected as 
representatives of the workers both in the bargaining and in the 
administration of the contract. While the union will obviously be concerned 
with a wide range of employment related issues, virtually all economic 
research on the behavior of unions has focused on the determination of wages 
and employment. Thus, the discussion here will concentrate on these 
dimensions of union behavior, and other issues will be discussed largely as 

10. Note that this definition excludes such cartels as the organizations 
of doctors, lawyers, barbers, or other tradesmen who organize in order to 
further their own interests through mechanisms other than collective 

they are relevant to understanding union wage and employment policy. 

It 15 use-ful at thi5 point to make clear the conception of the general 
mode of operation of a labor union in the American economy that is at least 
implicit in most economic research on labor unions. Unions are fundamentally 
organisations that seek to create or capture monopoly rents available in an 
industry. These rents could come from product market imperfections or from 
regulation of the industry. Alternatively, the union could organise a 
significant portion of the labor in a competitive industry and act as a 
monopolist in the sale of labor, creating and capturing rents from the product 
market. Entry by low cost nonunion firms would be prevented by the threat to 
organize new entrants. 

Good examples of unions which have historically operated in each of 
these modes are easy to find. The United Automobile Workers (UAW) is a union 
that thrived in the past on its ability to exploit market imperfections that 
existed in the American automobile industry and to ensure that the entire 
industry was organized. Recently, they are having considerable difficulty 
maintaining their position due to the increased competitiveness of the 
automobile industry that resulted from the shift in preferences of American 
consumers toward types of automobiles that are produced in other parts of the 
world. However, the workers in other countries (excluding Canada) are not 
unionizable by the UAW so that the UAW can no longer control the supply of 

labor in the automobile industry broadly defined. 

Another example is the airline industry. The various unions in that 

industry were able to achieve high wages with little resistance from the 


11. See H. Katz (1983, 1984) for more detailed analyses of the history and 
problems of the UAW and the automobile industry. 

12. Kahn (1980) presents a description of collective bargaining in the 
airline industry. 


airlines because the airlines knew that -fares and routes were regulated and 
that the regulatory agency would pass through any increases in costs to the 
■flying public. All airlines -flying a particular route were required to offer 
the same -fare. The primary harm to the airlines -from high wages resulted from 
the likelihood that fewer people and less freight would fly at higher prices 
as consumers switch to other modes of transportation. However, this sort of 
intermodal substitution is certainly more difficult for consumers than 
substitution among airlines. With the recent deregulation of the airline 
industry, new entrants who are nonunion can undercut the prices of the 
established union airlines resulting in substitution of nonunion airlines for 
union airlines by fliers. Once, again, the unions no longer control the supply 
of labor in their industry. Note that exactly the same analysis can be 

applied to the International Brotherhood of Teamsters (IBT) with regard to the 

recent deregulation of the trucking industry. 

A final example concerns the United Mine Workers (UMW) and the 

bituminous coal industry. This industry was characterized by a fragmented and 

competitive product market. The product was differentiated largely on the 

basis of location, as coal has a very high weight to value ratio making 

transportation relatively expensive. The UMW organized virtually the entire 

industry in key locations so that these firms as a group had local market 

power. The union exercised that market power by raising wages uni-formly. New 

entry by large firms was discouraged by the threat of unionization of the new 

entrants. The changing (declining) role of coal in the economy and the rise 

of strip mining has reduced the ability of the UMW to make a credible threat 

of organization upon entry of new firms. The result has been a declining 

13. See Levinson (19B0) for a description of collective bargaining in the 
trucking industry. 


position -for the UMW within the coal industry. 

These examples have been selected to highlight the importance of the 
market and institutional constraints within which unions operate. They truly 
set the bounds on what unions are able to achieve. Essentially, the tradeoff 
is one of wages versus employment. In situations where the union is able to 
gain market power by one means or another, they may be able to raise wages 
without substantial consequences for employment. On the other hand, as the 
examples show, such market power may be a fragile thing. An important focus 
of this study is the analysis of how a labor union that is faced with a given 
set of constraints makes decisions regarding its wage and employment policy. 

The wage-employment outcomes of collective bargaining are determined by 
the behavior of three actors: 1) the firm, 2) the union workers/members, and 
3) the union leaders. The first step toward an economic analysis of 
bargaining outcomes is defining the objectives of each of these actors. It is 
straightforward to model the firm as a profit maximizer. The union members 
can be assumed to have standard utility functions of the sort usually used in 
the analysis of individual behavior. For the purpose of this analysis, 
workers' utility is assumed to be function of income/consumption. That the 
union leaders have an objective function that deviates in any way from the 
objectives of the union as a whole is a relatively controversial and 
undeveloped notion. Most analysts have ignored any independent role for the 

14. See Farber (1978b, 197Sc) for a more detailed analysis of the wage 
policy of the UMW and its long term implications. 

15. It is standard in labor economics to have utility be a function of 
leisure (the complement of hours of work) as well as of income. Leisure is 
ignored here as not being central to the analysis of union behavior. Little 
is lost through this simplifying assumption. Oswald (19B2) presents an 
analysis of union objectives where leisure is an explicit argument in the 
workers' utility functions. 

16. At this point it is impossible to be explicit about the the objectives 
of the union as a whole. Indeed, this depends crucially on the preferences of 
workers and leaders as well as on the political process that governs the 

preferences o-f union leaders and have considered the union to be a reflection 
of the members preferences alone. Nonetheless, it seems reasonable that 

union leaders have well defined objectives and that they are constrained by 

the political process of the union. 

Early debate over the behavior of labor unions revolved around the issue 
of whether it is useful to model unions as having a coherent objective 
function that they attempt to maximize. This debate can be interpreted as 
turning on the relative importance of economic and political considerations in 
the determination of union wage policy. The relevant economic considerations 
are the constraints imposed by the labor market and employer response to the 
wage bargain (the labor demand schedule). The relevant political 
considerations ars the way in which the preferences of the workers, the 
preferences of the union leaders, and the market constraints interact to yield 
the wage policy (objective function) of the union as a whole. 

Ross (1948, p. 8) took the position that the wage policy of unions ". . . 
is not to be found in the mechanical application of any maximization 
principle." Ross goes on to argue (p. 14) that ". . . the typical wage bargain 
(with certain significant exceptions) is necessarily made without 
consideration of its employment effect." Ross claims further (p. 14) that the 
economic environment in the collective bargaining relationship operates ". . . 
at the second remove . . . CI]t generates political pressures which have to be 
reckoned with by the union leader." Indeed, these internal political 
pressures are central to understanding the behavior of unions in Ross's 
framework. These pressures have two sources. The first is differences in 

uni on. 

17. Exceptions to this are Ross (1948), Berkowitz (1954), Atherton 
(1973), Martin (1980), and Faith and Reid (1983). 

18. Some possible maximands for the leaders are the size of the union, 
dues revenues, and dues revenues net of the costs of running the union. 


interests between necessarily heterogeneous workers. The second, and perhaps 
more important in Ross's estimation, is the difference in interests between 
the workers and the union leaders. Ross is not clear on the precise nature 
o-f the interests o-f the workers, but he argues (p, 16) that organizational 
survival is the ". . . central aim o-f the leadership." 

In contrast to Ross's view of union behavior is the view, taken by 
Dunlop (1944, p. 4) and most economic analysts since, that " Lain economic 
theory of a trade union requires that the organization be assumed to maximize 
(or minimize) something." While he goes on to say that the standard case is 
one of wage bill maximization subject to the constraint imposed by the labor 
demand function, the force of his argument is that union behavior is amenable 
to analysis using the economists standard tools of optimizing behavior. 
Indeed, much subsequent work on the behavior of unions has been aimed at 

presenting alternatives to the wage bill as the appropriate maximand for the 

union. •, 

It is clear that a truly useful analysis of union behavior must address 

both economic and political factors. It seems appropriate to consider the 

union as a whole to be attempting to maximize a well defined objective 

function constrained by product and labor market considerations. It is likely 

that the behavior of both the leadership and the rank-and-file are affected by 

labor and product market considerations as they affect employment and the size 

of the union. At the same time the political considerations are central in 

determining exactly how the preferences of the workers and the preferences of 

19. The list of such studies is too numerous to detail here. Some of the 
more influential work includes that of Fellner (1949), Simons (1944), Cartter 
(1959), and Pen (1959). Surveys of the literature are contained in Atherton 
(1973) and Oswald (19B3). Recently some empirical work has emerged that 
implements models of union wage determination in order to investigate the 
nature of the union objective function. This work is discussed in more detail 
in section V. 


the leaders interact with each other and with the economic environment to 
yield the objective function -for the union. 

III. The Structure o-f Bargaining and the Efficiency of Labor Contracts 

Two types of bargaining structures will be considered. The first type 
is where the union and the employer bargain over the wage leaving the employer 
free to set employment. The second type is where the union and the employer 
bargain over both the wage and employment. These are polar cases of a more 
general model where the parties bargain over the wage and some aspects of 
employment. For example, it may be the case that the parties agree on a set 
of work rules that specify manning requirements or minimum crew sizes. Such 
work rules do not actually control the level of employment. They are closer 
to a specification of the capi tal -1 abor or output-labor ratio. 

Consider first the preferences of the employer. Let the firm's profits 
be a function of wages and employment holding product market conditions and 
the cost of capital constant. This function is 

(1) JI = II(W,L) 

where W is the wage rate and L is the level of employment. A higher wage 
raises costs which will make the employer, who faces a downward sloping demand 
curve for the product, raise price and reduce output. Thus, profits are 
monotonical ly declining in the wage ( H^ < 0). With regard to employment, 
there is a unique optimum level of employment conditional on the wage. 
Partially differentiating the profit function with respect to L and setting 
the result (H ) equal to zero yields the familiar downward sloping demand 
curve for labor. This relationship, 

(2) L = L(W) , 

defines the profit maximizing employment level at any wage. As the wage rises 


employment will fall not only because of the reduction in output caused by 

higher prices but also because the employer can substitute capital for labor 

in the production process. 

It is useful to ask what the isoprofit curves of the employer look like 

in wage-employment space. Their slope is simply 
dW H 

While 1I„ is always negative, the sign of H, depends on the values of W and L. 
The labor demand function was derived by setting H = 0, and it is clear that 
n. is negative (positive) if the wage-employment pair lies above (below) the 
labor demand schedule. Thus, each isoprofit curve is concave from below and 
has zero slope at the point where it crosses the labor demand schedule. 
Curves closer to the horizontal (L) axis represent higher profit levels. 
Figure 1 contains a representation of isoprofit curves with these properties 
along with the associated labor demand schedule. 

While it seems that the firm would prefer a wage that is as low as 
possible, it is constrained by the need to attract workers to the firm. 

Assuming that the workers have alternative jobs available at a wage W , the 

- a 

employer must pay at least that much or no workers will accept employment with 
the firm. Thus, the optimal wage from the firm's point of view is W and the 
optimal employment level is L(W ). In terms of the isoprofit diagram in 
figure 1, this pair is defined by the tangency between an isoprofit curve and 
a horizontal line at W . No isoprofit line yielding more profit will allow 
the firm to pay the wage (W ) required to attract workers. This is precisely 
the outcome that would occur in a competitive labor market with no union. 
Note further that this wage-employment pair is optimal from the employer's 
standpoint regardless of the structure of the bargain. 

In order to begin the discussion of the union's behavior, all questions 


o-f how the union's objective function are derived from the preferences of the 
workers and union leaders through the political process are deferred until 
later. Assume that the union has a well behaved objective function of the 

(4) U = U(W,L) 

where both W and L have a positive effect on union utility. Consider first 
the case where the parties bargain only over the wage and leave the employer 
to select the level of employment. In this case the optimal wage (W ) from 
the union's point of view results from maximization of this objective function 
with respect to wages subject to the constraint implied by the labor demand 
function. Transformation of the first order condition for a maximum yields 


(5) TT = - L' (W) . 

which implies that the optimum is where the union's marginal rate of 

transformation of employment for wages is equal to the slope of the labor 
demand schedule. The union has negatively sloped indifference curves in wage- 
employment space, and the highest indifference curve the union can reach when 
constrained by the labor demand schedule is that one which is tangent to the 
labor demand schedule. This is illustrated in figure 2. 

In the case described here, where bargaining takes place only over the 
wage rate and the employer has discretion over employment, the bargaining 
conflict is apparent in the firm wanting to pay a wage W to the workers while 

this is the absolute minimum that the union can accept and still remain in 

existence (attract members). It must be true that the optimal wage from the 

union's point of view is larger than W . 

20. If there are costs of union membership then the minimum survival wage 
required by the union will be higher than W by the amount necessary to cover 
these costs. ^ 


In the case where the employer and the union bargain over both the wage 

and the level o-f empl ovment , the employer will pre-fer the same combination 

(W , L(W )) as in the earlier case. However, the optimal wage-employment 
a a 

bargain from the union's point o-f view is a-ffected by the structure oi the 
bargain. The union would like as high a wage and employment level as 
possible. The question is what the constraints on these values are. Clearly, 
the union cannot -force the employer to continue operation with negative 
pro-fits or pro-f i ts . 1 ess than some minimum. Denote this minimum pro-fit level 
by I . The problem for the union is to maximize its utility with respect to W 
and L subject to the constraint that 

where the profit function is defined in equation (1). On this basis the 
optimal wage-employment bargain from the union's point of view is defined 
implicitly by the equality of the union's marginal rate of substitution of 
employment for wages and the employer's marginal rate of substitution of 
employment for wages along with the minimum profit constraint defined in 
equation (6). The first condition is 

(7) fT^ = i^ . 
Geometrically, the optimum is defined by the tangency between an indifference 
curve of the union and the firm's isoprofit line denoting profits of t^. This 
is shown in figure 3. 

Aside from the obvious difference in the most preferred bargains from 
the union's point of view as a function of the structure of the bargain, there 
is another aspect of the problem that is highlighted. It is clpar that where 
the parties bargain over both the wage and employment the most preferred 

position of the union is efficient in the sense that neither the firm nor the 

union can be made better off without making the other party worse off. 


However, where the parties bargain only over the wage the most pre+erred 
position of the union is not efficient. 

An important lesson can be drawn from this. Bargaining over the wage 
alone will not generally permit an efficient outcome. '^'^ In this case the 
union 15 acting as a simple monopolist and the standard sort of inefficiency 
arises. The employer will act conditionally on the bargained wage and select 
an employment level that is on the firm's labor demand schedule. The locus of 
efficient bargains (the contract curve) is derived in a straightforward 
fashion as the set of tangencies between the union's indifference curves and 
the firms isoprofit curves. Recall that the labor demand schedule is the 
locus of points that lie on isoprofit curves at points of zero slope in wage- 
employment space. Thus, if the indifference curves of the union are downward 
sloping everywhere in wage-employment space then no tangency between isoprofit 
and indifference curves will lie on the labor demand schedule and a simple 
wage bargain can never be efficient. Figure 4 contains a graphic 
representation of the contract curve (CO along with the labor demand schedule 

H the parties can bargain over employment (either explicitly or 
implicitly) as well as the wage, then any wage-employment outcome is feasible. 
This includes inefficient and well as efficient bargains. The economist's 
presumption is that where enough policy instruments exist for an efficient 

political nature of the union. What is at issue is efficiency regarding the 
profit function of the firm and the objective function of the union as a 
whole. The preferences of the workers and the union leaders are considered 
only indirectly through the union objective function. There may be important 
distributional consequences within the union that would suggest different 
definitions of efficiency. 

22. This notion has a long history. See, for example, Leontief (1946) and 
McDonald and Bolow (19B1) . 

23. Note that the contract curve can have any slope. It is drawn is figure 
4 with a negative slope for no particularly compelling reason. The shape of 
the contract curve will be discussed further in section V. 


outcome the outcome will, in fact, be e-fficient. However, given our relative 
lack oi understanding of the bargaining process, the efficiency of labor 
contracts must remain an empirical question. The conclusion is that 
bargaining over both wages and employment is a necessary but not sufficient 
condition for an efficient labor contract. 

Do unions and employers bargain over employment as well as wages? There 
are examples of declining industries or industries/occupations with declining 
employment as a result of technological change where employment guarantees 
have been negotiated. However, it is difficult to think of examples of 

industries with stable or growing employment where such guarantees have been 

negotiated. The more cominon situation is either no control over employment 

or the negotiation of work rules that attempt to control the capi tal -1 abor or 

labor-output ratio. One well known example is the set of work rules which 

existed for many years in the longshoring industry and specified minimum crew 

sizes and sometimes included the requirement that workers actually handle 

individual pieces of cargo regardless of the technology in use. If fully 

effective, work rules could lead to an efficient outcome depending on the 

nature of the technology and the product demand function. It is an empirical 

issue as to whether work rules in a particular situation are a sufficient 

instrument to remedy the inefficiency inherent in the standard wage 

24. Oswald (1984) presents evidence regarding the extent of explicit and 
implicit agreements concerning employment in ongoing collective bargaining 
relationships based on examination of a sample of contracts and a survey of 
large unions. The results are consistent with the view that bargaining over 
employment is uncommon. 

25. With the advent of containerized cargo, the requirement that workers 
actually handle each piece of cargo resulted in "stripping and stuffing" where 
each container was unpacked and repacked on the dock. The result was a 
reduction in both the quantity of shipping and employment in the ports where 
the union maintained such rules. The unions were forced to modify their rules 
in the end. 

26. Some attempts at tests of the structure of the bargain by Ashenfelter 
and Brown (19B3) and MaCurdy and Pencavel (1984) are discussed in section V. 



Why do virtually no labor contracts specify an e-f-ficient combination o-f 
wages and employment? A convincing argument can be made that e-fficient labor 
contracts are not feasible. Consider two types of efficient contracts. The 
first is an incentive compatible efficient contract where the employer, left 
to his own devices, would hire the efficient quantity of labor. This form of 
an efficient contract would specify that workers be compensated directly by 
employers at some wage rate which would imply a level of employment consistent 
with the labor demand schedule. In order to ensure "enough" employment, this 
wage rate is likely to be low in the sense that the union needs more revenue 
at that employment level to yield an efficient outcome. The firm would then, 
as a supplement to wage payments, make a lump sum payment to the union which 
is not contingent on employment. The union leaders would then have to 
distribute the lump sum payment to the members of the union. Two political 
problems for the union arise. First, the union may not have any mechanism to 
restrict membership so that anyone may claim a share of the lump sum 
payment.^ More importantly, the internal political process of the union may 
be such that those members with a controlling voice are those members who will 
be employed even when the wage rate is considerably above the efficient wage. 
These members would prefer an inefficient bargain with a higher wage and no 
lump sum transfer unless the union would make larger lump sum payments to 
these workers. However, it is likely that the union will have difficulty 
finding a stable mechanism for making different lump sum payments to different 

27. The problems that arise in such a distribution are identical to those 
that arose recently when the government of Alaska wanted to make lump sum 
distributions to their residents from royalties received for North Slope oil. 
At first they established a rather lengthy residence requirement for 
eligibility, but new arrivals challenged this in court and won. A much 
shorter requirement was imposed, and a much smaller royalty was paid to many 


members. These considerations suggest that the political process that governs 

the union may preclude incentive compatible eHicient contracts. 

One could argue that ef-ficient contracts that are not incentive 

compatible are feasible. This is the second type o-f efficient contract. In 

this type of contract the wage is set above the opportunity wage so that no 

lump sum payments are required and the employment level is set (either 

explicitly or implicitly) at the efficient level where the value of marginal 

product of labor is less than the wage rate. However, the employer left to 

his own devices would prefer to reduce the level of employment. Clearly, the 

employer will either have to be entirely precluded from adjusting the size of 

the workforce or have to be monitered very closely. Neither of these options 

is likely to be feasible. Given that demand will vary ovc-r time and that it 

would be exceptionally costly to the firm not to be able to adjust the size of 

the workforce in response to demand shifts, the firm will require some 

discretion in setting employment. In addition, it is likely that shifts in 

demand will be very difficult for the union to moniter so that the employers 

will have the opportunity to "cheat" on any labor agreement by reducing 

employment and output below the efficient level while claiming that there has 

been a demand shift. In more formal terms, there is asymmetric information 

regarding the state of product demand, and this will force the use of 

incentive compatible contracts.'' 

Overall, incentive compatible efficient contracts, where workers are 

more individuals. 

28. Consistent with this argument is the fact that it is difficult (if not 
impossible) to think of examples of unions (or firms) compensating workers on 
any basis other than time worked or output. 

29. Chatterjee (1982) presents a formal analysis of the difficulty in 
reaching efficient contracts where there is uncertainty. Grossman and Hart 
(1981) and Hart (1983), among others, present models of implicit contracts 
with asymmetric information more generally that are relevant to the arguments 

paid in addition to compensation received on the basis o-f wort: per-formed, may 
not be feasible due to the political diHiculties involved for the union in 
niakinq the additional payments. On the other hand, incentive incompatible 
e-f-ficient contracts, which speci-fy both the wage rate and the level o-f 
employment, may be precluded due to the asymmetric information held by the 
firm regarding the state of demand. We are likely to be left with inefficient 
labor contracts of the type generally observed, where the wage rate is 

determined through collective bargaining and the level of employment is set by 

the employer who is constrained to some extent by work rules. 

IV. The Bargaining Problem 

The discussion in the previous section highlighted the most preferred 
outcomes of the union and the firm. These objectives are to some extent in 
opposition to each other, and the observed outcomes will not in general be 
precisely the most preferred outcome of either party. Some further structure 
is needed to specify how the preferences of the parties are translated into 
bargaining outcomes. In virtually all private sector collective bargaining 
relationships in the United States, if the parties cannot reach agreement on 
the terms of the contract a strike occurs. The workers lose income and the 
firm sacrifices output and profits. Fundamentally, disagreement imposes costs 
on both parties so that there is an incentive for the parties to reach 

made here. 

30. Virtually all existing applied work proceeds under the assumption that 
unions bargain over wages and the employer selects the employment level 
without any work rule constraints. Although analysis of union decision making 
regarding work rules is an important area for future research, the discussion 
in succeeding sections of this chapter does not take formal account of work 


The bargaining problem is essentially one of the determination o-f price 
in bilateral monopoly. It is well known that the solution to this problem is 
indeterminate in the most general case. An early determinate solution that 
has been widely cited is that proposed by Zeuthen (1930) as extended by 
Harsanyi (1956). This solution is based on the notion of sequential 
concessions made by the parties until agreement is reached. The key to the 
model is an ad hoc process that determines which of the two parties will 
concede at any point. The details Are not important here except to say that 
the solution has the property that it maximizes the product of the incremental 
utilities of the parties. While the ad hoc concession rule is not 
convincing, the model is widely cited due to the fact that the solution is 
identical to the axiomatic model of bargaining outcomes derived by Nash (1950, 
1953) so that Zeuthen seems to provide a process justification for the later-, 
"rigorous" Nash model. 

The Nash model is probably the best known model of bargaining outcomes, 
and it has served as the basis for much work on axiomatic bargaining models. 
Essentially, a set of properties (axioms) that a solution should have are 
proposed, and the set of solutions that satisfy these axioms is derived. To 
the extent that the axioms are reasonable, the solution has appeal. Without 
going into any detail, the important axioms of the Nash model are 1) the 

31. This framework is directly applicable to collective bargaining in the 
private sector in the United States where the right to strike over economic 
issues in the setting of the terms of a collective bargaining agreement is 
largely unrestricted. In the public sector many jurisdictions have laws that 
prohibit some or all categories of public sector employees from striking. 
However, many of these jurisdictions have provided for arbitration of 
unresolved labor disputes involving public employees. Farber and Kats (1979) 
argue that arbitration imposes costs on the parties that have a similar effect 
in inducing agreement that the costs of a strike do. Bee also Crawford 
(1979), Farber (19B0a), and Farber (1981a). 

32. The incremental utility of a party is the difference between the 
utility of the proposed settlement and the utility if the parties failed to 
agree (the threat point). 

solution should be Pareto efficient; 2) the solution should be symmetric in 
that i -f the sets o-f incremental utilities o-f the parties are symmetric then 
the incremental utilities of the two parties at the solution should be equal; 
3) the solution should be independent of irrelevant alternatives in the sense 
that if all of the feasible outcomes of game A are contained in the set of 
feasible outcomes of game B and if the solution of game B is a feasible 
outcome of game A then it will also be the solution of game A; and 4) the 
solution should be unaffected by linear transformations of the utilities of 
the parties."' The strong result of Nash is that the only feasible solution 

that satisfies all of these axioms is the outcome that maximizes the product 

of the incremental utilities of the parties. 

The important point to note is that the Nash model and most other 

axiomatic models are normative rather than positive. They prescribe what an 

outcome ought to look like, and they are best considered prescriptions for 

arbitrators rather than a description of the likely outcomes of collective 

bargaining. Nonetheless, there have been some attempts to "test" the Nash- 

Zeuthen solution in the sense of seeing if actual negotiated agreements are 

consistent with the Nash model. A relatively crude empirical implementation 

of the model using aggregate data was done by de Menil (1971). Variables 

representing bargaining factors were found to be important, but little could 

be said about the precise form of the solution. Hamermesh (1973) implemented 

a test of the Zeuthen-Nash solution using disaggregated data, and he was not 

able to reach a definitive conclusion regarding whether the observed outcomes 

33. See Luce and Raiffa (1957) for a clear discussion of the Nash model 
and its axioms. Bishop (1963) and Roth (1979) present recent surveys of 
axiomatic bargaining models. Svejnar (19B3) presents a generalization of 
Nash's model that relaxes the symmetry constraint. 

34. In the case of symmetric utilities, this solution has the property 
that it results in an each party receiving an equal utility increment from the 
threat point. 


were consistent with the predictions o-f the model. A problem that Hamermesh 
recognized with his analysis is that the test is based on the extent to which 
outcomes "spl i t-the-di f ^ erence " between the initial o-f-fers of the parties. "^ 
This approach has two problems: 1) the initial oHers are subject to 
manipulation o-f the parties so that they are not good indicators of the threat 
point and 2) there is the implicit assumption that the utility functions of 
the parties are linear. Svejnar (1980) points out some of the problems with 
attempts to test the Zeuthen-Nash model, and he suggests an alternative that 
does not rely on information on the initial offers of the parties. However, 
it does require an explicit assumption regarding the form of the union's 
objective function. Indeed, a requirement of any implementation of the 
Zeuthen-Nash or any other particular solution to the bargaining problem is 
that a specification of the union's objective function must be assumed. The 
test then proceeds conditionally on this utility function. Most of the 
existing studies use a very simple assumption regarding the union utility 
function. The union is usually assumed to be a rent maximizer or to have a 
linear utility function. However, as is discussed in the next section, the 
existing evidence regarding union objective functions is not consistent with 
this view. 

An important weakness of the axiomatic models of bargaining is that they 
generally do not admit the possibility of strikes. There exists a body of 

35. Bognanno and Dworkin (1975) and Bowlby and Shriver (197B) implement 
similar tests using disaggregated data. 

36. It should be pointed out that all of the evidence discussed in the 
next section regarding union objective functions rely on arbitrary assumptions 
regarding the solution to the bargaining problem. 

37. The game theoretic models of bargaining that allow noncooperati ve 
behavior or mixed strategies in repeated games do allow for strikes. However, 
the notion of mixed strategies in this context is not terribly appealing. 
Fudenberg, Levine and Ruud (1983) present an interesting empirical analysis of 
a game theoretic model of bargaining outcomes with noncooperati ve behavior 
that admits strikes. 


literature that attempts to derive a determinate solution to the bargaining 
problem while at the same time admitting the possibility o-f a strike. These 
studies tend to rely on nations of relative bargaining power, bluHing, 
threats, investment, asymmetric information, uncertainty, and learning to 
explain the outcomes of collective bargaining. This literature is far too 
vast to survey here, but suffice it to say that most of the models do not have 
both the union and the firm behaving in ways fully consistent with optimising 
behavior.'" For example, while both parties may be attempting to optimize 
well defined objective functions, a determinate solution might be derived by 
imposing ad hoc rules for predicting the behavior of the other party or for 
learning about important facts. 

Two models of industrial disputes that have been widely cited and have 
served as the basis for much further analysis are those of Hick's (1964) and 
Ashenfelter and Johnson (1969). The Hicks model is well known for presenting 
a graph in wage-strike space of an upward sloping employer "concession 
schedule" and a downward sloping union "resistance curve". It is the 
intuitive appeal of this diagram, which seems to mirror the concession process 

that leads to agreement, rather than the precise behavioral underpinnings of 

the model that accounts for the popularity of the Hicks model. The union 

resistance curve gives ". . . the length of time [the workers] would be 

willing to stand out rather than allow their remuneration to fall below the 

3B. See the chapter by John Kennan elsewhere in this volume. Examples of 
models of the sort described here include Pen (1952), Bishop (1964), Cross 
(1965), Shackle (1957), Hicks (1963), Ashenfelter and Johnson (1969), and 
Johnston (1972). Bishop (1963) and Coddington (1968) presents surveys of some 
of this work. 

39. Hicks does not interpret the diagram as representing concessionary 
behavior. It is, in his view, an ex ante representation rather than a dynamic 
view of the concession process. See Comay, Melnik, and Subotnik (1974) for an 
attempt at empirical estimation of employer and union concession schedules. 
Farber (1980b) presents a more detailed discussion of Hicks's model than there 
i s room for here . 


corresponding wage." (Hicks, 1963, p. 142.) This curve is downward sloping 
because the sacri-fice involved in accepting a lower wage is larger so that 
workers will be willing to endure a longer strike to avoid such a reduction. 
The eraployer concession schedule is defined more precisely by Hicks. It is 
the seguence o-f wage-strike pairs such that "... the expected cost o-f the 
stoppage and and the expected cost o-f concession . . . just balance." (Hicks, 
1963, p. 141.) This is upward sloping by construction because at a higher 
wage the cost o-f concession is higher and a longer strike is also more costly. 
Clearly, the employer concession schedule is based on eguality o-f total costs 
rather than the sorts o-f marginal considerations that would signify an 
optimising model. While it may seem natural to interpret the intersection of 
the resistance curve and the concession schedule as the likely outcome of 
bargaining, there is no reason to think that this will be true. 

Ashenfelter and Johnson (1969) develop what could be considered a 
logical reformulation of the Hicks model. They argue that the union has a 
"concession schedule" in wage-strike space that is downward sloping and 
represents the minimum wage (increase) acceptable to the union at after a 
strike of a given length. It is downward sloping because it is likely that 

the privations endured by the workers as a strike wears on will reduce their 

militancy and make them willing to settle for less. The innovation in the 

A-J model is that the employer is modeled as being a niaximiser of the present 

discounted value of profits subject to the constraint implied by the union 

concession schedule. Essentially, the employer determines the optimal strike 

length by equating the marginal cost of continuing a strike (marginal foregone 

40. Ashenfelter and Johnson claim that an important element of their model 
is that the union leadership plays a central role both in mediating between 
the employer and the rank-and-file and in helping to enlighten the rank-and- 
file regarding what is a realistic demand. However, this does not seem 
central to their analysis. 


pro-fits) with the marq i nal benefit of continuing a strike (marginal decrease 
in the present value of the wage bill). The model explains not only the 
optimal strike length but also the wage outcome and whether a strike occurs at 
all. A number of important results can be derived from this model, and 
Ashenfelter and Johnson use the model to help specify and interpret the 

estimates of an aggregate time series regression analysis of strike activity 

in U. S. manufacturing. Farber (1978a) implements a structural version of 

the model using microeconomic data on individual bargains both across firms 

and over time. The strength of the A-J model is that it allows the firm to 

act in a manner fully consistent with profit maximization while yielding a 

determinate and plausib.le analysis of the the outcome of collective 

bargaining. The weakness of the A-J model is that the behavior of the 

workers/union is naive and not derived from an optimizing model of individual 

or union behavior. 

As should be clear from the discussion in this section, there is a long 

way to go toward a realistic and empirically tractable model of the outcomes 

of collective bargaining that allows for fully rational behavior on the part 

of all the actors. Progress has been made generally by denying full 

rationality at some point in the bargaining process and by assuming 

particularly simple forms for the union objective function. The latter is 

crucial because it seems that without a specification of the union objective 

function it is not possible to identify the process that leads to a particular 

41. Pencavel (1970) presents a similar analysis for Great Britain. 

42. See Farber (1977) and Farber (1981b) for other microeconomic analyses 
using the A-J model. Hamermesh (1970) presents an early analysis of the 
outcomes of collective bargaining using microeconomic data though without an 
explicit model of the process by which the agreement is reached. Farber 
(19B0b) presents an extension of the A-J model that introduces uncertainty 
about the union concession schedule and derives the optimal set of offers for 
the firm to make in this situation. 


bargaining outcome. At the same time, what led to the discussion in this 
section is that it does not seem possible to identify the objectives o-f the 
union without specifying a priori what the process that leads to a particular 
bargaining outcome. Indeed, for the investigations of union objectives 
surveyed in the next section, this dilemma is "solved" by assuming a very 
simple bargaining rule: the union can impose whatever settlement it wishes. 

V. Empirical Investigations of Union Objectives 

There has recently been great interest in estimating models of union 
behavior based on maximization by unions of well defined objective functions. 
Some of these, including studies by De Menil (1971), Rosen (1970), and Nickell 
and Andrews (1983), use aggregate data to estimate reduced form models of 
wage-employment determination in the union sector. While interesting in their 
own right, these studies are limited in the degree to which they can shed 
light on the nature of union objectives and the process by which agreement is 
reached. More interesting in this regard are some recent studies using 
disaggregated data that focus on the nature of the union objective function as 
it affects wage and employment determination. These studies include Farber 
(197Bb, 1978c), Dertouzos and Pencavel (1901), Carruth and Oswald (1983), 
Pencavel (1984a, 19B4b), Ashenfelter and Brown (1983), and MaCurdy and 
Pencavel (1984). What these studies have in common is that they focus on 
particular industries and they solve (avoid?) the difficult problem of the 
solution to the pure bargaining problem in similar ways. Farber (197Bb, 
197Bc) and Carruth and Oswald (1983) analyze the objectives of unions in the 
U. S. and British coal industries respectively. All of the other studies 
focus on the objectives of the International Typographer's Union (ITU) in its 
relationships with American newspapers. All of the studies assume that the 


union can impose whatever settlement it wishes on the ■firm so that the 
observed wage outcome represents the outcome that is most pre-ferred by the 
union. The studies di-f + er in what they assume about the structure o-f the 
bargain and in the extent to which the union objective function is derived 
■from the pre^ferences of the members and the political process within the 
union . 

The conceptual underpinnings o^f this literature date at least to the 
work of Dunlop (1944), Leontief (1946), Fellner (1947), and Cartter (1959) all 
of whom present models of union behavior where the union attempts to maximize 
a well defined objective function. In this early work the firm is assumed to 
maximize profits and the structure of the bargain is assumed to be such that 
the parties bargain over the wage while the employer is free to set employment 
according to the labor demand function of the firm/industry. Thus, the union 
is assumed to be a utility maximizer with respect to wages subject to the 
constraint embodied in the labor demand function. Dunlop (1944) argued that 

the appropriate raaximand for the union is the wage bill although he 

entertained some alternatives, including rent maximization. The others are 

less explicit about the particular maximand. No attempt is made in this early 

literature to derive the union objective function from the preferences of the 

individual workers or the political process within the union. 

Oswald (1982) presents a model of a "utilitarian" union that has an 

objective function that looks very much like rent (in utility units) 

maximization. In this model all of the workers within the union are assumed 

43. The wage bill is defined as the product of employment and the wage 
rate while rents are defined as the product of employment and the difference 
between the union wage and the opportunity wage of the workers. 

44. More recently, Atherton (1973) attempted an extension of the early 
literature to account for individual preferences and the internal politics of 
the union, but the results are not entirely successful. 


to be identical (a common assumption) and the utility function o-f the union is 
simply the sum o-f the utilities o-f the individual workers. There is no 
explicit political model presented that would yield such a simple -form for the 
union objective -function. However, the empirical studies o-f Farber (197Bb), 
Carruth and Oswald (1983), and Ashen-felter and Brown (19B3) are based on 
empirical speci -f i cati ons that are more or less consistent with a utilitarian 
union. For this reason, it is worth considering in a bit more detail. Its 
objective function is 

(8) V = LU(W ) + (M - L)U(W ) . ■ 

u a 

where V is the union objective function, U ( • ) is the utility function of the 

representative worker as a function of the wage rate, L is union employment, M 

represents the membership of the union, W is the union wage, and W is the 
^ ^ ' u a 

opportunity wage of the workers. Essentially, L of the union members will 

be earning W and M-L will be earning W . The union objective function can be 
u - a 

rewritten as 

(9) V = L[U(W )- U(W ) ] + MU(W ) . 

u a a 

Clearly, the last term is simply a constant from the standpoint of union 

wage/employment policy. The relevant maximand is LLUCW )- U(W )]. If the 

u a 

individual utility function is linear in wages then maximization by a 
utilitarian union is simply rent maximization. H the utility function is 
linear and the opportunity wage available to the workers is zero then 
objective function is the wage bill. Given a nonlinear individual utility 
function, the objective function is rents in utility terms rather than dollar 
terms. If the alternative utility is zero then the union objective function 
is simply "total" utility. ^*^ 

45. Consideration of the determination of the size of the union is 
deferred to section VI. For the time being li is considered to be exogenously 

Another general form -for the union objective -function that has been used 

as the foundation oi some of the recent empirical work (Dertouzos and 

Pencavel , 19B1; Pencavel , 19B4a) is a modified Stone-Geary utility function. 

This objective function has the form 

(10) V = K [W - W*]^'[L - L*]*'. 

The relative value of 6 and ^ is an indicator of the relative importance of 

*■ t 

wages and employment in union objectives. The quantities W and L can be 

interpreted as the absolute minimum wage and employment levels that the union 

can tolerate. One interpretation of W is as the opportunity wage of the 

workers (Pencavel, 1984a). This is because it is unlikely that a union can 

survive if it negotiates a wage below the opportunity wage of the workers. 

There is no equally clear interpretation for L . This model also has some 

interesting special cases. If 6=1, ^=0, and W =0 then the objective is wage 

maximization (Simons, 1944). If i=l, ^=1, L =0, and W =W then the objective 


is rent maximization. Finally, if 6=1, y=l, W =0, and L =0 then the objective 
is the wage bill. The advantages of the Stone-Geary utility formulation 
include its tractability and flexibility. Its disadvantage for the purposes 
of this analysis is that there is no pretense of its being derived from the 
preferences of the individual workers through the political process that 
governs the union. 

A final objective function that has been used (Pencavel, 1984a, 1984b), 
but which will not be presented here in any detail, is the augmented addilog 
utility function. Again, this is a relatively flexible functional form that 
has many interesting special cases. It shares advantages and disadvantages 
with the Stone-Geary, though it is probably a bit less tractable in estimation 

46. Assuming that the individual utility can be normalized, one could 
define LI(W ) = for a single value of W . However, as W chanqed over time 
U(W ) would differ from zero. 

and a bit more -flexible. 

How are the models implemented, and what is found when the models o-f 
union behavior are implemented using disaggregated data? It is worth going 
through a number of the empirical studies in some detail paying particular 
attention to assumptions regarding the structure of the bargain, the 
specification of the union objective -function, and the central findings. 

Farber (197Bb) estimates a model o-f wage and employment determination in 
the bituminous coal industry in the United States in the period -from 194B- 
1973. It is argued that the United Mine Workers (UMW) had cartelized the 
industry and could impose whatever wage it wished on the essentially 
competitive firms in the industry who would be free to set the employment 
level according to the labor demand schedule. It is further assumed that all 
of the members of the union are identical except that they are of different 
ages so that they prefer different mixes between wages and fringe benefits in 
the compensation package. A median voter argument is used to derive the 

optimal mix in the compensation package as that preferred by the median aged 

member of the union. Each worker is assumed to have the same probability of 

having a union job so that the expected utility of a given worker is 

(11) E(U) = b(T . ) + [1 - hu(T ) 
M ui Ma 

where L is union employment, M is the membership of the union, T . is the 
total compensation per manhour of the i worker on the union job, and T is 
the alternative compensation level per manhour available to each worker. 
Essentially, total union compensation is a weighted average of the wage and 
per capita expenditures on fringe benefits where the weights are a function of 

47. This analysis raises important issues of how to deal with multiple 
objectives for a labor union. Blair and Crawford (19B1) show that the median 
voter equilibrium proposed by Farber does not exist in general. The problem 
of aggregation of heterogeneous preferences and the median voter model in 
particular are discussed in section VII. 


the age o-f the worker. The quantity L/M represents the probability that a 


Farber argues that the union will act as i -f it is maximizing the 

expected utility o-f the median aged member of the union subject to the 

constraint imposed by the industry labor demand -function. Thus, the level and 

mix of compensation will be set so as to maximize E(U) as defined in equation 

(11) substituting T for T where ra is the index of the median aqed member. 

urn ui - 

Given the assumption of exoqeneity of the size of the union (M) , 

multiplication of the expected utility in equation (11) by M yields exactly 

the utilitarian objective function proposed by Oswald in equation (B). In 

other words, Farber's objective function for the UMW would be the same as the 

objective function of a utilitarian union that had all members with 

preferences identical to those of the median aged member. Farber assumes that 

each individual had a constant absolute risk aversion utility function, and a 

measure of average hourly earnings elsewhere in the U.S. economy was used as a 

proxy for T . On this basis the first order conditions for the optimal level 

and mix of compensation were derived. The model is implemented using Full 
Information Maximum Likelihood (FIML) to estimate the first order conditions 
directly, the labor demand function, and a set of other relationships defining 
the labor and product markets for coal. 

The central result of Farber's research on the UMW with regard to the 
union's objective function is that the workers appear to be quite risk averse, 
with a coefficient of relative risk aversion of 3.0 or more. Even if one does 
not accept the literal interpretation of the model, this result suggests that 
the union places substantial weight on employment in setting its compensation 
policy. The special case of risk neutrality, where the coefficient of 
relative risk aversion is zero and which would imply that the union is 
maximizing rents, is strongly rejected. In other words, the UMW seems to have 

placed more weight on employment relative to compensation than rent 
maximization would imply. 

Carruth and Oswald (19B3) develop and estimate a model of the wage 
policy of the National Union o-f Mineworkers (NUM) in Great Britain over the 
period -from 1950-19B0. They adopt a utilitarian objective -function for the 
NUM where all of the members of the union are identical with constant relative 
risl; aversion utility functions. The union is assumed to maximize this 

objective function with respect to the wage rate subject to the constraint 

imposed by the labor demand function. Government unemployment benefits are 

used as a proxy for W . The model is implemented using FIML to estimate the 

two equation system consisting of the labor demand schedule and a first order 

condition for a maximum of the union objective function. 

The central finding with regard to the union objective function of 

Carruth and Oswald is that they find a significant degree of relative risk 

aversion (a coefficient of relative risk aversion of about .8), though less 

risk aversion than seems to be implicit in the compensation policy of the UMW 

in the United States. This difference in results may be due to the fact that 

Carruth and Oswald used government unemployment benefits to measure the 

alternative income available to workers while Farber used an actual earnings 

measure which is bound to be larger than unemployment benefits. Such a 

systematic difference in alternative income measures is likely to produce the 

48. The source of the labor demand function in this case is a bit 
different than in the standard case. The British coal industry was 
nationalized over the entire period under investigation. The National Coal 
Board (NCB) was set up to run the industry. It is not clear exactly what the 
objectives of the NCB were so that it is difficult to argue that the sort of 
labor demand schedule a profit maximizing firm would have is appropriate for 
the British coal industry over this period. 

49. Carruth and Oswald do find that alternative wages as measured by 
earnings elsewhere in the economy are a significant determinant of union wage 
policy, but it enters the worker's objective function in an ad hoc fashion. 
It is not clear how to interpret this result. 


observed di-fference in the degree o-f risk aversion even i -f preferences are, in 
■fact, identical. Nonetheless, even the lower degree oi risl; aversion found by 
Carruth and Oswald implies a greater weight on employment relative to wages 
than would be implied by rent maximization. 

Dertouzos and Pencavel (19B1) explore the wage policy of the 
International Typograhphi cal Union (ITU) in their relationships with 
newspapers in a number of American cities in the period from 1946-1965. The 
union local in each city negotiates its own bargain, and it is argued that 
within each city the members of the union are homogeneous. It is further 
argued that the union has a long and important democratic tradition so that 
there is little conflict between the goals of the leaders and the goals of the 
rank-and-file. On this basis, Dertouzos and Pencavel argue that the objective 
function of the union is that of a leader who ". . . is assumed to integrate 
the welfare of all the union members." (p. 1167). There is no discussion of 
exactly how this integration takes place. It is assumed that the union 
objective function derived in this fashion is of the Stone-Geary form 
described in equation (10). The union maximizes this objective function 
with respect to wages and employment subject to the constraint imposed by the 
labor demand function. The model is estimated by specifying a labor demand 
function along with the reduced form wage equation derived from the first 
order condition for a maximum of the objective function. The estimates 
presented are derived using FIML on this system of two equations. 

The wage bargains struck by the Cincinnati Post with the ITU are 
examined in detail by Dertouzos and Pencavel. They find that the union placed 
a large weight on employment relative to wages. In the notation of equation 

50. Pencavel (1984a) presents a further analysis of similar data using the 
Stone-Seary objective function and the same set of assumptions. 


(10), they estimated a value of i' greater than the value oi I. They are able 
to reject the special cases, imbedded in the Stone-Geary -formulation, oi rent 
maximization and wage bill maximization. They also carry out somewhat less 
detailed analyses of the waqe bargains struck by the ITU in a number o-f other 
cities. They key result is that preferences seem to vary substantially across 
cities. More specifically, the weight on employment relative to wages as well 
as the minimum acceptable wage (W ) and employment (L ) levels are quite 
variable. ^' 

Pencavel (19B4b) extends his earlier work with Dertouzos on the wage 
policy of the ITU to consider an addilog objective function for the union. 
This has the advantage of being flexible and yielding a particularly simple 
form for the marginal rate of substitution that is equated to the slope of a 
particular specification for the labor demand schedule at the optimum. This 
relationship is solved for the wage and estimated directly using nonlinear 
two-stage least squares (NLTBLB) where employment is treated as endogenous 
along with the wage. Once again, Pencavel finds substantial variation in 
preferences across different locals of the ITU. Tentative evidence is found 
that the larger locals have an objective function that may approximate rent 
fliaximization. The others seem to place relatively more weight on employment. 
Wage bill maximization is rejected in all cases. 

The set of studies that have been discussed thus far (Farber, 197Bb, 
1978c; Carruth and Oswald, 1983; Dertouzos and Pencavel, 1981; and Pencavel, 
19B4a, 1984b) all find that implicit in the union wage policies that were 
examined is a wage/employment policy that puts a relatively high weight on 
employment. Both the rent maximization hypothesis and the wage bill 

51. Pencavel (19B4a) presents a further analysis of ITU wage policy using 
the addilog objective function. 


maximization hypothesis are rejected in virtually every situation. 0-f course 
only a very few di-f-ferent settinqs have been examined: mineworkers in the coal 
industries in the United States and Great Britain and typesetters in the 
newspaper industry in the United States. Given the great dif-ferences that 
exist across industries both in the characteristics of workers and in the 
structure and institutions o-f collective bargaining, great care should be 
exercised in generalizing these results to other settings. This is 
particularly true in light o-f the evidence presented by F'encavel and Dertouzos 
(19B1) and F'encavel (1984a, 1984b) that even within the ITU there is great 
variation across locals in the objective -function of the union. 

While the studies discussed above have focused on the nature of union 
objectives, a pair of studies by Ashenfelter and Brown (1983) (A-B) and by 
MaCurdy and F'encavel (19B4) (M-P) have focused on the issue of the efficiency 
of labor contracts. Recall that it was argued in section III that an 
efficient contract would not be possible if all that was bargained over was 
the wage. Thus, an investigation of efficiency is, at least in part, an 
investigation of the structure of the bargain. Do unions and firms bargain 
over wages alone? Do they bargain over both wages and employment? If they 
bargain over wages and work rules, are the work rules sufficient to ensure 
that the outcome would be efficient? Both the A-B and the M-P studies use 
data on wages and employment from the ITU. The two studies use very different 
approaches to the problem and they come to essentially opposite conclusions. 

Ashenfelter and Brown specify a union objective function that is the 
expected utility of the representative worker where each worker has the same 
utility function and the same probability of working on a union job. This is 
identical to the objective function used by Farber (1978b) and described above 
in equation (11). It is also observational ly equivalent to the utilitarian 


utility function proposed by Oswald (1982). The general form of the 
efficiency condition is contained in equation (7) as the equality of the 
union's marginal rate of substitution of employment for wages and the 
employer's marginal rate of substitution of employment for wages. Assuming, 
as A-B do, that the profit function is simply the difference between revenues 
and labor costs, the efficiency condition is 

(12) V,,/V, = (W - R, )/L , . 

where V(W,L) is the union objective function, and R is the marginal revenue 
product of labor. In the specific case of the utility function used by A-B 
the efficiency condition is ■ , 

(13) [U(W) - U(W )]/U,,(W) = W - R, 

a W " L 

where U(') is the utility function of the representative worker. If the 

workers are risk neutral so that the U(') is linear, then the efficiency 

condition reduces to the equality of the marginal revenue product of labor 

with the alternative (opportunity) wage (R =W ). In this case the union 

objective function is rent maximization, and employment is set at the same 

level it would be in the absence of the union. This is the key property used 

by the A-B analysis because it suggests that employment will not be a function 

of the actual wage (W) but only of the alternative waqe (W ) so that the 

' - a 

contract curve (the set of efficient settlements) is vertical. Ashenfelter 
and Brown go on to argue that this condition will be approximately true for 
more general utility functions. However, it is clear that it can only be 
exactly true if the union utility function is a monotonic transformation of 
total rents. This is 

(14) V(W,L) = g([W-W ]L) 

total compensation used by Farber. 

53. This is consistent with the vertical contract curve suggested by Hall 
and Lilien (1979) . 


where g(') is an increasing function of its argument. 

Ashenfelter and Brown base their test of the efficiency of the wage 
employment bargains of the ITU on a test of whether employment is a function 
of the actual wage as opposed to the alternative wage. Of necessity, the 
validity of this test is conditional on the validity of the assumption that 
the union is maximizing rents (or some monotonic transformation of rents). 
Their empirical analysis suggests rather strongly that employment is 
significantly affected by the actual wage even after controlling for the 
alternative wage. This would seem to be strong preliminary evidence for a 
conclusion that contracts in the newspaper industry between the ITU and their 
employers are not efficient. However, it may be that rent maximization is a 
sufficiently bad approximation to union objectives in the industry that a 
vertical contract curve is not appropriate. 

MaCurdy and Pencavel set up two models. The first is the labor demand 
curve equilibrium model (LDEM) where a union sets the wage so as to maximize 
its objective function subject to the constraint imposed by the labor demand 
schedule of the firm. This is clearly not efficient. The second model is the 
contract curve equilibrium model (CEM) where the parties set wages and 
employment so that the general efficiency condition (equation 7) is satisfied. 
They derive the standard equilibrium condition in the LDEM model where the 
factors of production (including labor) are employed such that the ratio of 
their prices is equal to the ratio of their marginal products. They further 
show that the equilibrium condition in the CEM model is identical to that in 
LDEM model with the exception of an additional term in the former representing 
the marginal rate of substitution (MRS) of the union objective function. This 

term has the effect of making the ratio of the wage to the price of other 

factors exceed the ratio of marginal products in an efficient bargain. The 


empirical test of the two models proposed by M-P is essentially a test o-f the 
importance of the "additional term" in the equilibrium condition implied by 
the CEM model. 

In implementing their test, M-P assume that the MRS implicit in the 
union objective function is a nonlinear function of employment and a set of 
union (local) and time dummy variables. Some special cases of the MRS are 
integrated to derive the associated utility functions, and it is argued that 
the form selected is sufficiently general to admit a wide range of objective 
functions. MaCurdy and Pencavel find that the LDEM model is rejected by the 
data in the sense that the variables that make up the additional term seem to 
be important. They further argue that the CEM is supported by their data 
largely because the estimated MRS implies a quasi-concave objective function 
for the union. However, they agree that a rigorous test of the CEM model is 
not possible without making more restrictive assumptions regarding the form of 
the union objective function and its associated MRS. The conclusion to be 
drawn is that in the case of the ITU the wage-employment bargain is not 
characterized properly by a union selecting a wage to maximize its objective 
function subject to the constraint imposed by the labor demand schedule. One 
must be agnostic as to whether the contract is, in fact, efficient. 

What do the results of the A-B and the M-P studies imply for the 
structure of the bargain? It seems clear that the simple LDEM model that is 
the null hypothesis of the M-P study is not appropriate in the ITU case. At 
the same time the A-B results, though limited due to the restrictive 
functional form, suggest that labor contracts in the ITU case are not 
efficient. This is consistent with the M-P results which cannot, in fact, 

the employer would prefer to hire less labor at the given wage. The 
equilibrium is off the labor demand curve. 

distinguish between different departures from the LDEM model. A reasonable 
interpretation would be that the structure of the ITU's bargains is that the 
parties negotiate over wages and a set of work rules. However, there is no 
presumption that these work rules are sufficient to force the bargain to be 
efficient. The union has, at best, partial control over employment. A final 
note of caution is that the structure of the bargain, including the particular 
work rules, is situation specific, and there is little, if anything, in these 
studies that provides convincing evidence on the efficiency of labor contracts 
or the validity of the LDEM model outside the ITU's relationship with the 
newspaper industry. 

It is useful to ask if there is anything general that has been learned 
from existing empirical studies of union objectives. Optimists would answer 
in the affirmative that they have learned it is generally true that unions are 
sensitive to the employment consequences of their wage policies and that they 
put substantial weight on employment relative to wages. They would concede 
that the precise relative weighting is context specific. However, the 
pessimist would argue that such strong conclusions are unwarranted for at 
least two reasons. The first is that the assumption underlying all of the 
studies, that the union can impose whatever settlement it wishes on the 
parties, may well not be appropriate. The researcher ignores the bargaining 
problem through use of this assumption at the peril of mi sattr ibuting 
moderation in wages to union preferences as opposed to employer resistance in 
bargaining. This would make it seem as if the union was putting a higher 
weight on employment relative to wages than is, in fact, the case. All of the 
results regarding rejection of the rent maximization hypothesis and the high 
relative weight put on employment would be called into question. However, as 
mentioned in the previous section on the bargaining problem, it may not be 
possible to identify the form of the solution to the bargaining problem 

without assuming something about the structure of the union objective 
function. An interesting and important agenda -for future research is a 
careful exploration of exactly how much a priori structure has to be put on 
objectives and/or the bargaining process in order to learn something useful 
from bargaining outcomes about both union objectives and the bargaining 

The second reason for pessimism regarding any general conclusions that 
can be drawn from these studies is based on the likelihood that while workers 
may have similar preferences in different contexts, the structural, 
institutional, and political characteristics that govern collective bargaining 
are sufficiently variable that the union objective functions will differ 
considerably across contexts. What this suggests is that in order to model 
union behavior more generally, the process by which the individual preferences 
are aggregated into an objective function for the union must be considered 
carefully. Unfortunately, the studies surveyed here shed relatively little 
light on the relationships between worker preferences, the structural features 
of a union, the political process, and the union objective function. 

There are at least three important issues that must be addressed in 
order to derive a union objective function from the preferences of the workers 
and the political process of the union in a consistent manner: 1) the 
determination of the size and composition of the union; 2) heterogeneity in 
preferences among the membership; and 3) reconciliation of conflicting goals 
of the membership and leadership. These problems are interrelated, and how 

55. Another important issue relates to the conceptual problems introduced 
by a bargaining structure where the parties bargain over more than one issue 
(e.g., wages and employment) . Farber (197Bb, 197Bc) attempts to handle 
multiple objectives of the UliW in the context of a median voter model, but 
Blair and Crawford (1981) point out some problems with Farber's analysis. 
Voting equilibria with multiple issues exist where some special conditions 
regarding the preferences of the workers are met. However, these cases are 


one problem is addressed depends on how the others are addressed. All o^ the 
empirical research surveyed in this section embodies a set of implicit or 
explicit assumptions regarding these issues. In the succeeding sections each 
problem is discussed briefly in turn in order to indicate why they are 
important and to suggest potential avenues for analysis. 

V I . Size and Composition of the Union 

It IS commonplace to model the objective of a union as a function of 
wages and the level of employment. However, it is the membership of the union 
at the time the collective bargaining agreement is negotiated that 
participates in the decision making process. While the level of employment 
implied by the agreement may be indistinguishable from the ex post membership, 
the ex ante membership (at the time of negotiation) is likely to be very 
different. Thus, the role that the level of employment plays in the union 
objective function is not at all clear from the perspective of how that 
objective function might be derived from the preferences of the workers 
through whatever political process governs the union. The relationships 
between membership, employment, and how workers evaluate potential wage- 
employment bargains requires further examination. 

The decision of a worker regarding union representation has been modeled 

not intuitively appealing. See Riker (19B0). This general problem will not 
be discussed further here. 

56. It is likely that membership and coverage by a collective bargaining 
agreement are not the same thing even ex post . In states with Right-to-Work 
laws workers are not required to join a union or pay dues as a condition of 
employment. L. Katz (1983) presents evidence regarding the prevalence of 
covered-nonraembership in states with and without Right-to-Work laws. Lunsden 
and Peterson (1975), Warren and Strauss (1979), Wessels (1981), Ellwood and 
Fine (1983), and Farber (1984) present analyses of the effect of Right-to-Work 
laws on the extent of unionization. 

as a utility maximizing decision based on a comparison by the worker of the 
utility on a union job and on a nonunion job. Union wage-employment policy 
is directly relevant to the decision of an individual regarding whether to 
join a union because it affects how a potential member values a union job. 
The importance of the wage is obvious. The level of employment is relevant to 
the extent that union employment is related to the wort;er's evaluation of the 
likelihood of getting a scarce union job and sharing in the advantages of 
unionization. Thus, an important factor in determining the size and 
composition of the union is how scarce union jobs are allocated among the 
membership. In discussing allocation schemes it is assumed that the parties 
negotiate over the wage and that the employer is free to set the level of 

Note that whether a union job is scarce depends in part on the mechanism 
used to allocate union jobs. Lewis (1959) made a distinction between the 
allocation rules used by what he called boss-dominated and employee-dominated 
unions. He argued that boss-dominated unions allocate jobs using the price 
mechanism. For example, the level of dues might be adjusted so as to 
eliminate the excess demand for union jobs. On the other hand employee- 
dominated unions allocate jobs with nonprice mechanisms such as random 
assignment, jobsharing, seniority, nepotism and the like. In the boss 
dominated union most of the advantages of unionization are realized by the 
leadership, while in an employee-dominated union most of the advantages of 
unionization are left for at least part of the membership. Evidence 
consistent with the employee-dominated model is presented by Abowd and Farber 
(1982) and Farber (19B3a) who find that there is excess demand by workers for 

57. See, for example, Lee (1976), Farber and Saks (1980), Abowd and Farber 
(1902) , and Farber (1983a) . 


union jobs. Thus, the discussion o-f allocation rules here revolves around 

nonprice mechanisms. Any analysis o-f boss-dominated unions is more properly 

deferred until the discussion of the reconciliation of the preferences of the 
membership and leadership in section VIII. 

A simple job allocation rule is one which allows the jobs to be 

allocated randomly so that each member has the same probability of having a 

job after the wage is determined. This rule implies that each member has a 

probability of employment equal to the ratio of labor demand to existing union 

membership (L/M) . Assuming that if a worker is not employed on a union job 

then the worker will work on an alternative job at W , the representative 


worker's expected utility is 

(15) E(U) = ^U(W - C) + Li - bu(W ) 
li u Ma 

where union employment (L) is an inverse function of the union wage and C 
represents the cost of continued union membership. The expected utility of 
individual members is inversely related to the size of the membership because 
as the union grows each worker has a smaller probability of being selected in 
the lottery for union employment. However, it is straightforward to 
demonstrate that the most preferred wage of each worker is not affected by the 
size of the union (M) . 

Workers will make their choice regarding union membership on the basis 
of a comparison of E(IJ) and U(W ). The condition for preferring union 

membership is that 


„U(W - C) + [1 - ^]U(W ) > U(W ) , 
M u Ma a 

and it is clear that all workers will prefer union membership as long as W -C 

r u 

is greater than W . Thus, the union will expand which implies a dilution of 

58. This is the rule that is explicit in the work of Farber (197Bb, 197Bc) 
and Ashenfelter and Brown (19B3). 


the benefits of unionization. Where workers differ in their alternative wage 

only those workers with alternative waqes below W -C will desire union 
' ' u 

membership and the marginal member of the union will be indifferent between 

union membership and employment at the alternative wage. 

One possible alternative to a random assignment for the allocation of 
jobs would be an equal sharing of available work so that all members are 
guaranteed at least some work. A somewhat more complicated objective function 
for each worker is required because implicit in work sharing is the notion 
that hours are variable. Assume that all workers have identical preferences 
defined over income (Y) and the fraction of the standard workday (or week, 
month, year) worked (H) . fiepresent these preferences by the function 

(17) U = U(Y,H) 

where income has positive marginal utility and hours of work (the complement 

of leisure) has negative marginal utility. The representative worker's 

utility on a union job is 

(IB) U=U(WH-C,H) 
u u 

where H represents the fraction of time worked with pure work sharing which is 
simply the ratio of labor demand to union membership (H=L/M). Net income on 
the union job is the product of the fraction of time worked and the wage rate 
less the cost of union membership (C). 

The size of the membership has important effects on the level of utility 
in the work sharing model, though in an ambiguous fashion. An increase in the 
membership means less income which reduces utility. On the other hand it 

59. The implications of heterogeneity in the alternative wage for union 
policy is discussed further in section VII. 

60. Implicit in the random assignment model is that employers hire workers 
■for a fixed number of hours which is the same both in union employment and in 
alternative jobs. Thus, there was no need to consider the labor - leisure 
tradeoff explicitly. 


means more leisure which increases utility. Note that it would normally be 

expected that a larger membership would mean more division o^ the "spoils" o-f 

unionization and less utility. However, that is not necessarily the case here 

because it is assumed that workers are not -free to set their hours at the 

optimal level for a given wage. Their hours are completely determined by the 

wage rate through the labor demand schedule and the size o-f the union. Unlike 

random assignment, the optimal wage is not independent o-f the size oi the 

union where there is work sharing. Workers make their choice regarding union 

membership on the basis o-f a comparison of U and U(W ). The condition -for 

u a 

preferring union membership is that . '■ 

(19) U(WH-C, H)>U(W,1) 
u a 

noting that on the alternative job the worker will work standard hours (-full 

time). H workers are identical and union work was -full time, all workers 

would desire union representation as long as W - C was greater than W . What 

u a 

this suggests is that at a given wage the size o-f the union will expand so 
that the degree o-f work sharing makes workers i ndi -f -f erent between union 
membership and employment on the alternative job. H workers 
heterogeneous in their alternative wage then only those workers with low 
alternative wages will desire union membership and the size o-f the union will 
expand so that the marginal worker (the worker in the union with the highest 
alternative wage) is indifferent between union employment and working full 
time at the alternative wage. 

Two factors limit the settings in which random assignment and 
worksharing schemes are feasible. The first factor is highlighted by the 
previous discussion regarding the dilution of the benefits of unionization if 
the union is open to anyone who wishes to join. On this basis, it is clear 
that neither random assignment nor worksharing is likely to be feasible unless 
the union has an effective mechanism for excluding workers from union 


membership and eligiblity for union work. The second factor is based on the 
{act that it is likely that workshanng is more easily implemented over 
periods longer than a week or month through rotation of workers through jobs. 
This sort of workshanng can be accomplished by periodically reallocating 
jobs, perhaps randomly. Thus, there is an element of workshanng even in 
random allocation schemes. On this basis, random assignment or work sharing 
is likely to be found only where workers have long run attachments to the 
union rather than to the employer. If workers had long run relationships with 
particular employers then the initial draw from the lottery for union jobs in 
a random assignment scheme would have long run implications that preclude 
workers from having additional chances at attaining a union job and sharing in 
the work. 

Examples of industries that are appropriate for random assignment or 
work sharing are the hiring hall industries best exemplified by the 
construction trades. These unions historically have had effective 
mechanisms to limit membership through stiff skill requirements that could be 
met through apprenticeship programs which allowed only limited enrollment. In 
addition, construction jobs are necessarily of limited duration, and the 

workers have long run attachments the union. Job referrals from union run 

i 2 
hiring halls can be interpreted as a mechanism for explicit work sharing. 

The key to understanding the job allocation system in most union 

settings is that workers have job rights . Workers who are employed in 

particular positions are not forced to share those jobs with anyone else. Nor 

are they required to enter a lottery to keep their job. In this context 

61. See Haber (1945) and Mills (1980) for descriptions of collective 
bargaining in the Construction Industry. 

62. While dated, Haber (1945) presents examples of hiring halls enforcing 
work sharing through referals. 


workers who are not already working on a union job have little incentive to 
join a union and pay dues because joining gives them no rights to share in the 
advantages o-f unionization. The union will be composed o-f workers who are 
employed at a given time, and it is these workers who will make decisions 
regarding future wage-employment policy. The way most union contracts outside 
the hiring hall industries are structured, the employer has complete 
discretion in hiring when employment is growing. However, once the worker 
is hired (and is past some relatively short probationary period) the worker 
has a right to the job. Since wage increases will generally imply a decline 
(or smaller increase) in employment, it is crucial to specify how scarce union 
jobs are allocated when all workers have rights to their jobs. 

Perhaps the most widely used rule for the allocation of union jobs is 
based on accumulated seniority (Abraham and Medoff, 19B4a). Those workers who 
are more senior have priority. If there is a decline in employment then the 
workers are laid off in inverse order of seniority. Consider the case where 
workers have identical preferences and alternative wages and differ only in 
their position in the seniority hierarchy. Index workers by their position in 
the seniority hierarchy so that worker i is the i most senior worker. If 
there ars L workers employed at a given wage, the L most senior worker is 
just on the margin of being employed. All workers with less seniority than 
the L worker have no seniority and are equivalent from the standpoint of not 

63. Depending on whether or not there is a union security clause in the 
contract and whether or not there is a Ri ght-to-Wor k law in existence, these 
new workers may or may not be required to join the union or pay dues. 

64. Laid off workers often retain for a limited period of time rights to 
the jobs that they held. If there is a subsequent increase in hiring after 
layoff then the employer may be required to offer the new jobs to laid off 
workers in seniority order (the last laid off are the first recalled). 

65. This notation is due to Blair and Crawford (1981) who present a 
concise analysis of union wage behavior where there is uncertainty about labor 
demand and seniority is used to allocate jobs. 

having union employment. The utility of each of the L union workers is U(W-C) 

while all other workers have utility U(W ). 


There are two important implications of the seniority job allocation 
scheme that are relevant for the discussion here. The first is that the issue 
of excl udabi 1 1 ty versus nonexcl udabi 1 i ty of potential members is not 
important. Since all workers with zero seniority do not have a right to a 
union job, they represent no threat to dilute the benefits of unionization to 
the existing workers. In fact, this may be one reason why seniority rules ire 
so popular. The second important implication of the seniority job allocation 
rule is that workers of different seniority levels will have systematically 
different preferences regarding optimal union wage-employment policy. Workers 
with more seniority will generally prefer higher wages because their jobs are 
well protected by a buffer of less senior workers. The less senior workers 
are likely to prefer lower wages because they are more vulnerable to layoffs 
in employment declines. In the simplest possible static model where there is 
no uncertainty about labor demand, each worker will prefer the wage that puts 
that worker just on the margin of being employed. In other words, the i 
most senior worker will prefer a wage such that labor demand is just equal to 
i. In a more complicated model where there is uncertainty about labor demand 
(Blair and Crawford, 1981), the optimal wage for each worker is likely to be a 
monotonic function of seniority but not with such a simple relationship. If 
the workers are risk averse then it seems likely that they will prefer a wage 
such that the expected employment level implies a buffer of less senior 

The discussion in this section makes clear the important role of 
employment in determining the value to individual workers of union wage 
policy. More importantly, it suggests that the job allocation mechanism 
implies structural restrictions on how employment enters individuals' 


evaluations of union policy that ought to be exploited in generating an 
objective -function tor the union as a whole. While individual pre-ferences 
regarding wage-empl ovment policies under various job allocation schemes are 
relatively clear, nothing further can be said about how the union as a whole 
will behave with respect to wage-employment policy without specifying the 
political processthatgovernstheunion. 

VII. Heteroqenei ty in Preferences Among Workers -. 

If all workers have identical preferences regarding the appropriate 
union wage-employment policy then the preference aggregation problem is 
trivial. Assuming that there is perfect democracy so that the leadership 
cannot pursue its own goals independently, the union objective function will 
accurately reflect the objectives of the representative member. However, the 
assumption of homogeneous preferences is untenable in general, and the 
preferences of workers with regard to the optimal wage-employment policy will 
differ along a number of dimensions. The most important differences are 
likely to be: 1) workers having different labor market alternatives and 2) 
workers having different amounts of seniority as it affects their job security 
through the job allocation system. The risk associated with any wage- 
employment policy will vary systematically along both of these dimensions. It 
is likely that workers with better labor market alternatives and with more 
seniority will prefer higher wages. Clearly, some mechanism must be 
provided to aggregate the disparate preferences of the members into a coherent 

66. This claim is based on an implicit model where union labor demand is 
uncertain and workers are employed at their alternative wage if they do not 
have a union job. Blair and Crawford (19B1) present such a model where 
preferences vary by seniority. 

union objective function. 

The problem of preference aggregation is not unique to the analysis of 
union behavior. It arises in the context of public choice at all levels: How 
does a political process take the disparate preferences of individuals and 
translate them into public policy? In the context of this study, what is 
the political process that prevails within labor unions? It is perhaps a 
measure of how far analysis of this problem has yet to go that the only truly 
operational model of aggregation of individual preferences into a coherent 
objective function for a democratic organization is the median voter model. 

The median voter model was first formulated by Black (1948) and Arrow 
(1950). Assume that individual preferences are a function of only a single 
variable (e.g., wages), the quantity of which is to be determined through some 
sort of voting mechanism. Assume further that each individual's preferences 
are single peaked in this dimension so that there is only a single relative 
maximum in utility defined over the entire range of possible outcomes. A 
sufficient condition for this is that the utility function be globally 
concave. Assume further that the individuals' most preferred outcomes are 
distributed across the voting population in a well defined fashion. Under a 
set of reasonable conditions, it can be shown that the median most preferred 
outcome is the only position that will defeat all other positions in any 
sequence of pairwise elections. Thus, a candidate who adopts this position 
cannot be defeated in a pairwise election. This is called a voting 
equilibrium. The median voter is defined as that voter for whom half of the 
other voters have most preferred outcomes that are lower and half have most 

67. See Buchanan and Tullock (1962) for an early discussion of problems of 
public choice in a broader context. There is a large body of literature on 
public choice that is beyond the scope of this chapter to review. Some 
examples from this literature include Downs (1957), Arrow (1963), Plott 
(1967), Fishburn (1973), and Riker (1980). 


pre-ferred outcomes that are higher. More importantly, it can be shown that i-f 

any of the basic assumptions of the model fails then no position will e;;ist 

that can defeat all other positions. In such a case the outcome will depend 

on the order in which the various options are presented for voting and control 

of the agenda becomes crucial. From the standpoint of the discussion here, 

the most important assumptions are 1) single peaked preferences; 2) a single 

issue being decided; 3) no imposition of outcomes other than through voting 

(nondi ctatorshi p ) ; and 4) pairwise elections. 

As a simple illustration of the median voter approach to the analysis of 

union wage policy consider the case where workers differ in their productivity 

and hence in the alternative waae (W ) available to them. Assume that jobs 


are allocated randomly and that the size of the union is fixed. Each worker's 
expected utility is defined in equation (15). It is straightforward to show 
both that these preferences are single peaked under standard conditions 
regarding the utility and labor demand functions and that the optimal wage of 
each worker is a monotoni cal 1 y increasing function of W . Thus, the 
conditions for a voting equilibrium are satisfied, and the objective of the 
union is to provide the wage that maximizes the expected utility of the worker 
with the median alternative wage. 

What are the implications of this outcome? First, as one would expect, 
unions with higher median skill levels will have higher optimal wages. More 
importantly, the optimal wage depends only on the median skill level and not 
on any other characteristics of the distribution. H the distribution is 
skewed so that there are some members with very low alternative wages, these 
workers will have a particularly large advantage from unionization. On the 
other hand, if the distribution is skewed so that there are some members with 
very high alternative wages, these workers will have a particularly small 
advantage from unionization. In fact, the alternative wage for these high 

productivity workers may be larger than the equilibrium union wage so that the 
high productivity workers will leave the union. The result will be a drop in 
the median alternative wage and a reduction in the union wage. This cycle 
will be repeated until at some point an equilibrium will be reached in both 
the size o-f the union and the union wage. 

The implications of this model are consistent with two types of 
observations. First is the well known standardization of rates within 
industrial unions resulting in a large union-nonunion wage differential for 

unskilled workers and a smaller union-nonunion wage differential for skilled 

workers in this sector. Second is the set of internal political problems 

that exist in unions, such as the United Automobile Workers (UAW) , with a 

skewed skill mix. For example, the skilled tradesmen within the UAW have 

historically been unhappy with their relative lack of influence on union wage 

policy. They have felt that they could do better if they negotiated on their 


The UAW example also shows the limits of the median voter formulation. 

The UAW must accommodate the high skilled workers in order to keep them in the 

union and in support of union policy. While beyond the scope of this 

analysis, it is likely that the bargaining position of the UAW would be weaker 

without the support of skilled workers crucial to the production process. In 

fact, it could be argued that the strategy of bargaining over percentage 

increase in wages rather than over wage levels themselves is in part an 

68. Many studies have documented the standardization of rates across skill 
levels within the union sector through the estimation of cross section 
earnings functions. See, for example, Bloch and Kuskin (197B), Freeman 
(1980b) and Lewis (1984). Even these studies exaggerate the variation in 
union rates for particular jobs within establishments because the estimates 
are made with very crude skill measures across establishments. Farber and 
Saks (1980) present evidence that can be interpreted as workers perceiving 
that unions standardize wage rates within establishments. See the Webbs 
(1920) for an early and insightful discussion of the importance of the 


attempt to maintain historic di -f f erent i al 5 between workers o-f diHerent skill 
1 evel 5. 

H the union uses seniority to allocate jobs then the most preferred 
wage of any particular worker will depend on that worker's seniority. In a 
static context where there is no uncertainty about labor demand, each worker 
will prefer a wage such that the worker is the least senior worker employed. 
Preferences are single peaked and the median voter equilibrium is to set the 
wage so that the median seniority worker is the least senior worker employed. 
This version of the median voter model implies a shrinking union over time. 
H there are initially M members then the union will have as an objective the 
optimal wage of the (M/2) worker. The optimal wage of this worker has the 
property that the worker is now the least senior worker employed in the in the 
union firm. The result is that the new membership of the union is M/2. When 
it is time to renegotiate the contract, the (M/4) worker is the median 
worker. The optimal wage of this worker will be higher yet so that this 
worker is the least senior worker employed. The union will again reduce its 
size by half, and this process will repeat itself until there are at most a 
handful of workers in the union. 

Of course, unions do not shrink out of existence so that there must be 
an element missing from this model. One element is that the union may not be 
able to achieve its objectives in bargaining due to employer resistance. The 
result will be a lower wage, more employment, and a larger union than desired. 
Another element is foresight on the part of the current median member. This 
worker must recognize that pursuing the wage policy described above will 

standard rate. 

69. See H. Katz (19B4) for a more detailed discussion of the influence of 
skilled workers within the UAW. 

70. Heterogeneity in alternative wages does not affect the thrust of this 


result in a loss o-f the union job in the -follDwinq period as e-f-fective control 
o-f the union passes to a more senior (or more skilled) worker. A more 
conservative wage policy may delay the time until the job is lost, but the 
only wage policy that will preserve the median member's control is to set the 
wage so that the entire initial membership is employed. 

An important consideration, neglected thus -far, that will limit the 
shrinkage of the median voter controlled union where jobs are allocated on the 
basis of seniority is uncertainty about the demand -for labor. In this 
situation, the worker with median seniority does not know with certainty the 
wage that will make the worker the least senior employee. It is worthwhile 
developing this model more f ul 1 y .-f ol 1 owi ng the analysis o-f Blair and Crawford 
(1981) . Let . 

(20) L(W) = G(W) + n . 

where E(W) represents the systematic part of the labor demand function and M 
represents a random element affecting labor demand with zero mean. The 
probability that a worker with seniority rank i will be employed on the union 
job (EMP.=1) at the wage W is ■ ,,,, 

Pr[E«P.=l] = Pr[L(W)>i]. 


= Pr[M>i-G(W)] 

= 1 - F(i-G(W) ) • 

where F(') represents the cumulative distribution function of H. The expected 
utility of worker i at union wage W is 


EU (W) = U(W . ) 
1 ai 

EU.(W) = {1 - F(i-G(W) )}U(W-C) + F(i-G(W))U(W ) 
1 ai 





where C represents the (dues and other) costs of unionization and W 


represents the alternative waqe of worker i. Assuming that W-C>W ., it is 
^ - ai 

straightforward to derive the the optimal wage for a worker with seniority i. 
Blair and Crawford (1981) derive sufficient conditions on the utility function 
and the distribution of M for the preferences of the workers to be single 

If all workers have the same alternative wage the median voter is the 
member with the median seniority level. This worker's seniority index is 
i=H/2. Note that the allocation rule could be defined over almost any 
dimension without altering the optimal wage at all. If the alternative wage 
varies across workers the situation is somewhat more complicated because the 
most preferred wage of each worker depends not only on seniority but also on 
the alternative wage. A voting equilibrium still exists, but it is not clear 
who the member with the median most preferred wage is. Workers with more 
seniority will certainly prefer a higher wage as will workers with a higher 
alternative wage. However, unless the distributions of seniority and 
alternative wages have the same rank ordering, the individual optimal wages 
will be monotonic in neither seniority nor the alternative wage. Preferences 
are still single peaked and a voting equilibrium exists, but, without 
information on the joint distribution of seniority and the alternative wage, 

71. In addition to the usual conditions regarding the concavity of U ( • ) , 
the sufficient conditions include a labor demand function concave in the wage 
rate and demand uncertainty (M) with a nondecreasi ng hazard rate. The hazard 
rate of « is defined as f (x ) / (1-F (x ) ) . Many common distributions, including 
the normal, have this property. 


it is imoossible to predict whose preferences will prevail. 

The dynamic implications o-f the median voter model with uncertain labor 
demand -for the size of the union are difficult to derive precisely. Blair and 
Crawford (19B1) show that the optimal wage of a given member declines as the 
worker's risk aversion increases. This is relevant here because it implies 
that risk averse workers prefer to set the wage so as to provide a cushion of 
low seniority workers who will be laid off first in the event of an 
unfavorable realization of the labor demand uncertainty (M). Thus, where 
there is uncertainty about labor demand, the median voter controlled union 
will not shrink to the same point as it would were there no uncertainty. 

The median voter model as derived here is a very powerful tool for 
aggregating the preferences of union members into a coherent objective 
function for the union as a whole. However, its applicability is limited due 
to the restrictive set of assumptions required. The most stringent of these 
for the purpose at hand are that only a single issue be decided and that there 
is perfect democracy. While the analysis of union behavior with multiple 
issues is not considered formally, the next section contains a discussion of 
the implications of conflicting goals of the union leadership and membership 
for the determination of union objectives. 

VIII. Conflicting Goals of Membership and Leadership 

The median voter model discussed in the previous section had as a basic 
assumption that the union was perfectly democratic in the sense that the 
leadership would be defeated immediately and costlessly if they strayed at all 

72. The median voter controlled union could even grow where there is 
uncertainty if there is an unexpectedly large realization of labor demand, 


•from the voting equi 1 1 bri um wage. Thus, the issue o-f leadership goals as 
distinct -from membership goals was not relevant. In -fact, the members might 
as well vote -for wage levels rather than for leaders. O-f course, the 
assumption o-f per-fect democracy is no more valid -for labor unions than it is 
for other political institutions. Union leaders sre free within certain 
limits to pursue their own goals. Many analysts, including Ross (1948), 
Berkowitz (1954), and Atherton (1973), have recognized the importance of 
imperfections in the democratic process and the concomitant consideration of 
the distinct goals of the leadership. Ashenfelter and Johnson (1969) develop 
a model of the outcome of collective bargaining that they argue is consistent 
with the view that the leadership and the rank-and-file have distinct 
expectations and objectives. More recently, Faith and Reid (1983) 
reformulated the problem as a princi pal -agent problem where the union 
leadership acts as the agent for the membership. The case where there is a 
perfectly operating democracy (as it is called here) is the case of no 
malfeasance in the pri nci pal -agent nomenclature. Similarly, the case of 
imperfectly operating democracy is a situation where malfeasance on the part 
of the agent is possible. 

fi major problem with the analysis of union behavior where the leadership 
has some freedom to pursue its own goals (malfeasance) is that very little is 
known about what these goals might be or how they might be analyzed in a 
systematic fashion. Ross (1948, p. 16) argues for ". . . the primary 
importance of organizational survival as the central aim of the leadership." 
However, beyond this there there is very little analysis, and saying that the 
primary goal of the leadership is to survive is really to say nothing at all 
about the goals of the leadership. It is obvious that the organization must 

survive if the leadership is to have a vehicle to pursue whatever its true 

aims are. 


It is not possible here to provide a theory o-f the objectives of union 
leadership. However, it is possible to gain some insight into union behavior 
by examining the constraints acting on the union leadership. The primary 
constraint on the union leadership is that they remain in power because 
otherwise they would not be able to pursue their objectives, whatever they 
might be. This is more than an empty -formalization. Essentially, limits will 
be set on how -far the leadership can deviate -from the interests o-f the 
membership, perhaps as reflected in a voting equilibrium. These limits will 
depend crucially on the friction in the democratic process. It may be that in 
some cases the limits turn out to be su-f -f i ci ent 1 y loose that the leadership 
can ma;-;imize their objective function without regard to the constraints o-f the 
political process (dictatorship). In other cases it may be that the 
leadership is severely constrained by the political process and the need to 
answer to the rank-and--f i 1 e. 

It is worth developing a simple version o-f this model more formally in 
order both to consider the potential of this approach and to highlight some of 
the difficulties in an analysis of this sort. Assume that the leadership is 
interested in having as large a union as possible. This objective for the 
leadership may be rooted in the desire to maximize the dues income of the 
union where dues are levied on a per capita basis. As before, the members get 
utility solely from their wage income net of dues payments, and the union 
bargains with the employer over the setting of a single wage for all workers. 
Workers may differ -in their alternative wage, and job allocation is on the 
basis of seniority if the net wage is such that the number of members who 

slowly over time so as to fully exploit its "capital", either on their own 
behalf or on behalf of the current members, before their inevitable departure. 

Leaders have finite lifetimes while organizations have (at least 
conceptually) infinite lifetimes. 

desire jobs is greater than the number of available jobs. Maximization of 
membership in this context is identical to maximization of employment where 

members who are not employed leave the union. The analysis proceeds 

conditional on a given dues level. 

If the democratic process in the union is operating perfectly, so that 
no malfeasance is possible, then the wage will be set at the voting 
equilibrium defined by the optimal wage of the median individual. The other 
extreme is the case where the leadership is completely unconstrained by the 
political process. In this situation, the leadership is constrained by two 
relationships. The first is the labor demand function of the employer (L(W)). 
This is a declining function of the wage rate, and it represents the maximum 
level of employment/membership at a given wage. The second constraint is a 
membership function of the sort proposed by Dunlop (1944). This is an 
increasing function of the wage rate net of dues, and it represents the number 
of members who want union jobs at a given wage. 

The membership function can be derived formally from the distribution of 

alternative wages among the members. Let i index worker's rank on the basis 

of their alternative wage where i=l represents the highest alternative wage. 

An individual will desire a union job if the wage (W) net of the costs of 

unionization (C) is greater than the alternative wage (W .). More formally, a 

- ai 

worker will desire a union job if W-C>W .. The membership function is 


(23) M(W-C) = t1 "KW-O 

where M represents the initial size of the union and ^(') represents the 

cumulative distribution function of W . among the initial membership. This is 

ai ' 

74. The case where the leadership is interested in maximizing dues income 
directly and sets both the wage and the dues level to that end is considered 
bel ow. 

J ■ .M'i.. 


clearly an increasing function of the wage rate. 

Because the union cannot coerce workers to join and cannot coerce the 
employer to hire workers, the quantity of employment at a given wage rate is 

(24) H(W,C) = MIN[L(W) ,M(W-C) ]. 

Given the negative slope of L(W) and the positive slope of M(W-C), the wage 
rate that maximizes employment is defined by the intersection of the labor 
demand and membership functions. This relationship is 

(25) L(W) = h(W-C) . 

Note that there is no job allocation problem because the number of members is 
equal to the number of jobs. The union will be composed of the least skilled 
workers among the initial membership, and all of the original members who have 
alternative wages greater than W-C will take jobs at their alternative wage. 
Now suppose that the union leadership is interested in maximization of 
dues revenues directly and that they can set the dues level as well as the 
wage. The objective function for the union leadership is 

(26) V(W,C) = CM(W-C) 

which is maximized subject to the constraint that only those workers who are 
employed become/remain members of the union. This constraint, embodied in 
equation (25), is simply that the membership of the union is equal to the 
labor demand of the employer. Without deriving the explicit relationships 
defining the optimal wage/dues pair, it is clear that at any wage rate the 
union leadership will raise dues to the point where the increase in dues 
revenues from existing members is just offset by the loss of dues revenues as 
membership declines. Once again, there is no job allocation problem because 
the number of members is equal to employment, and the union is composed of the 
least skilled workers. 

In both the case of the membership mazimizing union leadership and case 
of the dues revenue maximizing union leadership, the marginal worker will be 


i nd i -f f erent between union eiDDloyment and the alternative job (W =W-C), and 


all of the 1 nf ramarginal workers get a positive wage advantage from 
unionisation equal to W-C-W ., This result is very similar to that derived by 

o 1 

Lewis (1959) for his conception of a "boss-dominated" union. Lewis argued 
that the union leaders monopsonize the supply of labor and extract from the 
members all of the rents so that the members are indifferent between union 
employment and nonunion employment. However, he did not consider the 
possibility that different workers get different benefit from unionization so 
that a single wage and dues level cannot extract all rents. If the union 
leadership could set different wages or dues levels for different workers it 
would act -as a perfectly discriminating monopsonist buying labor from workers 
at their reservation price. Thus, the model developed here is an extension of 
Lewis's boss dominated union with heterogeneous workers. 

It 15 impossible to determine whether the wage net of dues (W-C) that an 
employment or dues maximizing union leadership sets will be higher or lower 
than a perfectly democratic union with a voting equilibrium would set. 
Detailed information on the labor demand function, the distribution of 
alternative wages, and the preference function of the union members would be 
required. However, the fact that there are likely to be more workers willing 
to work at the union wage than the union employer is willing to hire at that 
wage suggests that dues revenue and employment could be increased by some 
combination of increasing the dues level and reducing the wage in order to 
induce the employer to hire more workers. This is consistent with the 
notion that the net wage set by a dues revenue maximizing union leadership 

75. See Abowd and Farber (19B2) and Farfaer (1983a) for discussions and 
estimation of models of the determination of the union status of workers where 
there are queues for union jobs. Raisian (1981) presents evidence suggesting 
the the levels of dues and fees in most unions do not offset the union- 
nonunion wage differential. 

with no political constraints would be below that implied by a voting 
equilibrium. Certainly, it is clear that it would only be by accident that an 

un-fettered leadership would set wages and dues equal to that which would arise 

out of a per-fectly operating democratic union. 

The perfectly opearatinq democratic union and the completely un-fettered 
leadership run union are two extreme views that are unlikely to be a perfect 
reflection of any real union. The attractiveness of the two types of models 
presented thus far is not their congruence with the operation of actual labor 
unions, but it is the ease with which these models can be operationalized. 
Indeed, virtually all empirical work on the behavior of labor unions surveyed 
in section V at least pays lip service to the model of the perfectly 
democratic union. While no one has attempted to analyze union objectives as 
the result of an unfettered leadership pursuing it own goals, this would 
certainly be feasible. It is an open question as to the relative empirical 
performance of these two extreme models. 

While it is impossible to characterize completely a model of union 
behavior with a "somewhat" imperfect democracy, it is useful to at least lay 
out the barest outlines of such an approach. Consider the case where the 
leaders are elected through a process that is both costly and uncertain. By 
costly it is meant that potential candidates or insurgent groups must spend 
time and/or money in attempt to defeat the current leadership. In addition, 
it is not certain ex ante whether the insurgency will succeed. As before, 

76. The role that dues play in a perfectly democratic union has not been 
considered directly to this point. Essentially, this is a dimension in 
addition to wages that the members have preferences over, assuming that the 
level of union services (grievance handling, etc.) is a direct function of 
dues revenues in a democratic union. This raises all of the complicated 
problems of a multiple issue voting process. 

77. At certain times and in certain unions the costs of mounting an 
insurgency have been much higher and more immediate. 


assume that workers diHer in their alternative wages, that jobs are allocated 

based on seniority when there are more members than union jobs, and that dues 

are fixed. If there is a perfect democracy then the voting equilibrium is 

where the wage is set at the level that maximizes the utility of the median 

member (the member with the median optimal wage) as derived above. Without a 

perfect democracy the union leadership has some freedom to pursue its own 

goals constrained by the knowledge that as they stray farther from the goals 

of the membership they are more likely, to be defeated. For the purpose of 

this discussion characterize the leadership goal as maximization of dues 

revenues which, with fixed dues, is identical to employment/membership 

maximizati on . . 

At the voting equilibrium wage (W ) only the median member feels that 
3 1 ^ m 

this is an optimal outcome. All other members feel that there is some other 

wage that would make them better off. The essence of the voting equilibrium 

is that W is the only waqe for which there does not exist some other wage 

that more than half the members prefer. Suppose that the leadership deviates 

from W in their pursuit of dues revenue maximization (or any other goal) and 

that they set the wage at W . Note that W may be greater or less than W . 

D D ~ m 

In this situation there is a set of wages, including W , of which all the 

' m 

elements are preferred by at least half the workers to W 


If there are more workers who would like a job at W than the employer 


is willing to hire, then the membership/dues maximizing union leadership will 
attempt to set the wage below W so as to induce the employer to hire more 
workers. In this situation all of the members of the union with optimal wages 

above W will be worse off and all of the members with optimal wages below W_ 
m B 

will be better off. Some of the group of workers whose optimal wage is 

between W^, and W will be better off and some will be worse off. The 
B m 


important question is whether those workers who are worse off -find it in their 

interest to form a coalition to defeat the leadership. It seems reasonable 

that what the coalition can offer a worker is a reduction in the distance 

(where the metric is expected utility) between the union wage and the worker's 

optimal wage. The larger the reduction in distance the more the worker will 

value the coalition. Denote this value function by H(W,W.,W„) where W., the 

1 B 1 

optimal wage of the i worker, embodies all of the information about the 

individual including the level of seniority and the alternative wage. 

The total gain to the coalition net of the costs of formation of the 

coal i t i on is 

(27) H = E H(W,W. ,W„) - K 
1 B 

where the summation is over all members of the potential coalition and K 

represents the costs of formation of the coalition. There is likely to be 

uncertainty on the part of the incumbent leadership about the ultimate net 

gain of a coalition. Given that a coalition will be formed only where the net 

gain is positive the incumbent leadership will be uncertain as to whether a 

particular coalition will, in fact, form. The leadership can compute a 

distribution for the total gain for each possible coalition, and from this 

they can compute the probability that at least one coalition will form. The 

central feature of this model (conjecture at this point) is that coalitions 

will be more likely to form the larger is the total gain to the members of the 

coalition. It is certainly true that the incumbent leadership can influence 

the total gain from any coalition by manipulating W which implies that they 

can influence the probability that at least one coalition will form. Since 

the benefit from leadership is also a function of W^,, the incumbents can 

7B. This will be true whether coalitions are organized by aspiring leaders 
out for personal gain or by groups of workers who will share the gain. 


compute the expected beneHt -from leadership as a function o-f W as the 

product of the probability that no coalitions form and the benefit from 

continued leadership. On this basis they can compute the value of W that 


maximizes the expected benefit from leadership. This is the wage that the 

union will set where there is "imperfect" democracy. , . 

Although they is not demonstrated formally here, there are a pair of 

substantive results that emerge from this model. First, the existing 

leadership will deviate more from the voting equilibrium position where 

insurgencies are more costly (K is larger). Lower costs make insurgencies 

more likely, and the leadership will compensate for this with a more popular 

wage policy. Second, the position promised by the insurgency (and delivered 

by the union if K is small) will be relatively close to the voting equilibrium 

position. This is more difficult to make intuitive, but consider a union with 

three members. The optimal wages of the three workers are W , W =2W. , and 

W =3W . The voting equilibrium wage is clearly W^ , but a union leadership may 

not feel bound to provide this wage. If the leadership provides a wage that 

deviates only slightly from W^, say W slightly lower, then an insurgency 

could promise an improvement to the last two workers but not to the first. 

However, the maximum to improvement to the last two members (at some wage 

slightly higher than W ) will be relatively small. The insurgents cannot 

raise the wage very far above W without losing member 2 to the incumbents. 


This small gain is not likely to cover the cost K of forming the insurgency. 
On the other hand, if the leaders set the wage at a very high level, say 
W =W , then there will be substantial gain to the insurgency. Any wage lower 
than W, is preferred by both member 1 and member 2, and the gain is likely to 
be quite substantial. For example, the voting equilibrium position (W ) is a 
dramatically different position from W that members 1 and 2 are both likely 


to prefer strongly to W =W,. Dl course, these conclusion rest on strong (but 
reasonable) assumptions about the expected utility -functions o-f the members. 
Overall, unless the barriers to an insurgency are very high the existing union 
leadership will set the wage relatively close to the voting equilibrium so as 
not to encourage insurgencies. 

The conclusion that even with imperfect democracy a union is not likely 
to stray far from the voting equilibrium has important implications for 
evaluating the recent popularity of a casual sort of median voter model to 
describe union behavior. The use of the median voter concept in this area has 
ranged from formal use as a voting equilibrium (Farber, 197Bb; Blair and 
Crawford, 19B1) to more widespread use as a general description of unions as 
organizations that satisfy "average" members while labor markets cater to 
"marginal" workers (Freeman and Medoff, 1979, 19B3; Freeman, 19B0a, 19B1; 
Medoff, 1979). It is clear that a pure median voter equilibrium exists only 
under very special conditions that are unlikely to be met in the context of 
labor unions. However, the argument made in this section provides a more 
general justification for the approximate descriptive validity of the median 
voter concept. 

The discussion in this section demonstrates the power of even relatively 
simple models of the goals of members and leaders to generate testable 
implications regarding union behavior. Clearly, a fruitful area for further 
theoretical and empirical research relates to the problems of aggregation of 
individual preferences, particularly where workers are heterogeneous and the 
democratic process is not perfect. More specifically, with further work it 
may be possible to isolate the institutional features of particular unions 
that affect the ease with which insurgencies can form and their effect on 
union wage-employment policies. 


Overall, the research surveyed in this chapter illustrates the 
substantial progress that has been made in the analysis o-f union behavior. At 
the same time, there remains an extensive agenda for -further research that 
needs to be addressed before economists can claim a real understanding of 
union behavior. 



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Abraham, Katharine G. and James L. NedoH. "Length o-f Service and Probability 
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Farber, Henry S. "Individual Preferences and Union Wage Determination: The 
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Farber, Henry S. "The United Mine Workers and the Demand -for Coal: An 

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Farber, Henry S. "The Union Status of Jobs: Some Preliminary Results," mimeo, 
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Figure 3 

Figure 4